Pienaar scored Everton's goal and contributed a fine all-round display
Everton produced an assured performance to draw with Sigma Olomouc in the Czech Republic and confirm their place in the Europa League group stages.
The Toffees, leading 4-0 from the first leg, had Tony Hibbert sent off for a foul on Jakub Petr and Lukas Bajer hit the bar from the resulting free-kick.
But they responded well and Steven Pienaar converted Leon Osman's cross with a fine strike to open the scoring.
Pavel Sultes swept in an equaliser from distance but Everton eased through.
The draw for the group stages takes place on Friday at 1200 BST but David Moyes's men will otherwise turn their attention back to domestic events.
With two defeats - and just one goal scored - in as many games, they host Wigan on Sunday desperate to kick-start their Premier League season.
Moyes would have been pleased with his team's overall performance against a talented Olomouc side, especially considering that from the sixth minute onwards they played with 10 men in scorching temperatures.
He will also be delighted by the return of Yakubu, who was introduced off the substitutes bench after 10 months out with an Achilles injury, and also handed a debut to 17-year-old midfielder James Wallace.
Everton were boosted before kick-off by the news that a deal had been agreed to sign Portsmouth defender Sylvain Distin, but it seemingly did little to rouse the starting XI.
As in the first leg, when they were forced to weather a spell of sustained Olomouc pressure, the Toffees looked some way off the pace during the opening exchanges.
Petr, unfortunate not to receive a penalty when the sides met at Goodison Park, collected possession deep inside opposition territory and surged towards goal.
The 19-year-old striker weaved through the middle of a flat-footed Everton defence and, were it not for a reckless late tackle by last-man Hibbert on the edge of the box, he would have been one-on-one with Tim Howard.
French referee Fredy Fautrel was left with no choice but to give Hibbert his marching orders but the punishment ended there for Everton as Bajer's curling set-piece rebounded off the woodwork and was cleared to safety.
The visitors were under pressure and Tomas Horava sent a thunderous drive wide of Howard's right-hand post before Tomas Janotka miscued his shot from what looked like an offside position.
But Olomouc would be made to regret their profligacy and Everton soon took control of proceedings.
The architects of their progress were Osman and Pienaar, the latter providing an enticing cross from the left with which on-loan striker Jo narrowly failed to connect.
On the half-hour mark Ladislav Onofrej had a penalty shout correctly rejected after he was cleanly challenged by Marouane Fellaini.
Fellaini, along with impressive fellow-midfielder Jack Rodwell, was beginning to have a greater influence on proceedings but it was Osman and Pienaar who combined to put Everton ahead.
Osman broke free on the right and raced towards the byline before picking out Pienaar with an inch-perfect centre.
The South African produced a neat piece of control with his left foot before lashing the ball past a helpless Tomas Lovasik with his right.
Arriving shortly before the break, the goal ended any hopes Olomouc harboured of a unlikely comeback and they were barely given a sniff in the second half.
Everton dominated possession and, despite creating few chances of their own, comfortably kept the hosts at bay.
That was until Leighton Baines felled Rudolf Otepka and, instead of crossing, the Czech midfielder rolled his free-kick inside for Sultes to squeeze a first-time shot through numerous bodies and into Howard's bottom right-hand corner.
The home crowd came to life but it was too little too late and the night belonged to Everton.
Everton manager David Moyes: "It was a job well done. I am pleased we got through, it was important for us. I thought we got better as the game went on.
"They put us under pressure but thankfully we defended well enough and got one ourselves.
"It was disappointing to see Tony get sent off and that affected us. I thought it was a wee bit harsh, I have seen them (red cards) given and seen them not.
"But in Europe, if you misplace passes you will put your defenders in trouble and you will probably end up making rash tackles which will be punished."
75:01 Rudolf Otepka takes a long range shot clearing the crossbar.
74:20 Pavel Sultes takes a shot. Save made by Tim Howard.
74:12 The ball is crossed by Rudolf Otepka.
72:03 Phil Neville restarts play with the free kick.
72:03 Substitution Pavel Sultes replaces Tomas Janotka.
72:03 Substitution Rudolf Otepka comes on in place of Lukas Bajer.
72:03 Dan Gosling fouled by Michal Ordos, the ref awards a free kick.
71:26 Foul by Silva Daniel Rossi on James Wallace, free kick awarded. The free kick is delivered left-footed by Leighton Baines
from left wing, save by Tomas Lovasik.
70:48 Free kick awarded for a foul by Marek Kascak on Jose Baxter. Free kick taken by Phil Neville.
69:46 A cross is delivered by Marek Kascak, Header from deep inside the penalty area by Michal Ordos goes harmlessly over the crossbar.
69:11 Jose Baxter is flagged offside by the assistant referee. Indirect free kick taken by Ales Skerle.
67:22 Unfair challenge on Ales Skerle by Joao Alves Jo results in a free kick. Free kick taken by Tomas Lovasik.
66:51 Effort from a long way out by Ales Skerle goes wide right of the target.
66:16 The ball is sent over by Silva Daniel Rossi, Ladislav Onofrej takes a shot. Phil Neville gets a block in.
65:11 Substitution James Wallace joins the action as a substitute, replacing Steven Pienaar.
65:11 Substitution Jose Baxter joins the action as a substitute, replacing Leon Osman.
63:37 Shot from 25 yards from Marek Kascak. Save by Tim Howard.
63:14 Silva Daniel Rossi crosses the ball, clearance by Phil Neville.
62:37 The ball is swung over by Michal Ordos, Tim Howard makes a save.
60:48 Ales Skerle gives away a free kick for an unfair challenge on Joao Alves Jo. Leighton Baines takes the direct free kick.
58:32 Free kick awarded for an unfair challenge on Jack Rodwell by Michal Ordos. Free kick taken by Tim Howard.
57:14 Free kick awarded for a foul by Tomas Horava on Steven Pienaar. Free kick crossed left-footed by Leighton Baines from left
wing, save by Tomas Lovasik.
56:29 Unfair challenge on Leighton Baines by Tomas Janotka results in a free kick. Direct free kick taken by Leighton Baines.
55:52 The offside flag is raised against Michal Ordos. Free kick taken by Phil Neville.
54:07 Tomas Horava has an effort at goal from outside the penalty box which goes wide right of the target.
53:26 The referee blows for offside against Steven Pienaar. Ales Skerle takes the free kick.
52:40 Dan Gosling delivers the ball, save by Tomas Lovasik.
52:01 Silva Daniel Rossi challenges Steven Pienaar unfairly and gives away a free kick. Leighton Baines restarts play with the free
49:43 Michal Ordos gives away a free kick for an unfair challenge on Joseph Yobo. Direct free kick taken by Joseph Yobo.
48:24 Marek Kascak takes a shot from long distance which goes wide of the right-hand upright.
47:52 Unfair challenge on Lukas Bajer by Phil Neville results in a free kick. Free kick taken by Ladislav Onofrej.
46:25 Inswinging corner taken left-footed by Ladislav Onofrej, Header by Michal Ordos from deep inside the penalty area misses to
the left of the target.
46:15 Silva Daniel Rossi produces a cross, clearance made by Leighton Baines.
45:01 The referee gets the second half underway.
45:00+0:42 The match has reached half-time.
45:00+0:10 Marek Kascak takes a shot. Save by Tim Howard.
44:33 Dan Gosling challenges Jakub Petr unfairly and gives away a free kick. Tomas Horava takes the direct free kick.
42:26 Assist on the goal came from Leon Osman.
42:26 GOAL - Steven Pienaar:Sigma Olomouc 0 - 1 Everton Steven Pienaar finds the back of the net with a goal from inside the penalty box to the top right corner of the goal. Sigma
Olomouc 0 (0)-(5) 1 Everton.
41:51 Ladislav Onofrej gives away a free kick for an unfair challenge on Leon Osman. Free kick taken by Dan Gosling.
40:57 Free kick awarded for an unfair challenge on Joao Alves Jo by Tomas Horava. Phil Neville restarts play with the free kick.
39:52 Marouane Fellaini is penalised for handball and concedes a free kick. Pavel Dreska restarts play with the free kick.
39:06 Foul by Tomas Horava on Joao Alves Jo, free kick awarded. Leighton Baines takes the direct free kick.
37:29 Free kick awarded for a foul by Ladislav Onofrej on Leon Osman. Phil Neville crosses the ball in from the free kick.
36:49 Tomas Janotka is ruled offside. Tim Howard takes the free kick.
36:24 Free kick awarded for a foul by Joao Alves Jo on Ales Skerle. Ales Skerle takes the free kick.
36:04 Steven Pienaar sends in a cross, save made by Tomas Lovasik.
35:20 Steven Pienaar takes a inswinging corner.
34:40 The ball is sent over by Lukas Bajer, save by Tim Howard.
31:30 Foul by Tomas Janotka on Leon Osman, free kick awarded. Free kick taken by Phil Neville.
28:56 Tomas Janotka sends in a cross, clearance by Joseph Yobo.
27:52 Tomas Janotka takes a shot. Save by Tim Howard.
27:34 Marouane Fellaini gives away a free kick for an unfair challenge on Michal Ordos. Marek Kascak takes the direct free kick.
27:00 Tomas Janotka has an effort at goal from deep inside the area missing to the left of the goal.
25:50 Michal Ordos is ruled offside. Tim Howard takes the indirect free kick.
24:41 Inswinging corner taken from the right by-line by Ladislav Onofrej, Shot by Tomas Horava from just outside the area goes over
24:31 Outswinging corner taken from the left by-line by Ladislav Onofrej.
22:31 Ales Skerle restarts play with the free kick.
22:31 Booking Caution for Dan Gosling.
22:27 Tomas Horava fouled by Dan Gosling, the ref awards a free kick.
21:41 Free kick taken by Phil Neville.
21:41 Booking Ladislav Onofrej booked for unsporting behaviour.
21:34 Ladislav Onofrej concedes a free kick for a foul on Leon Osman.
20:03 Corner taken left-footed by Ladislav Onofrej from the right by-line, clearance by Phil Neville.
19:48 Ladislav Onofrej takes a inswinging corner.
16:57 Centre by Steven Pienaar.
14:59 Free kick awarded for an unfair challenge on Joao Alves Jo by Ales Skerle. Direct free kick taken by Phil Neville.
12:51 Ladislav Onofrej concedes a free kick for a foul on Leon Osman. Jack Rodwell takes the direct free kick.
11:37 Leighton Baines fouled by Michal Ordos, the ref awards a free kick. Leighton Baines takes the free kick.
9:33 The ball is delivered by Ladislav Onofrej, free kick awarded for an unfair challenge on Tim Howard by Michal Ordos. Tim Howard
restarts play with the free kick.
8:43 Drilled right-footed shot by Tomas Janotka. Save by Tim Howard.
7:47 Effort from just outside the box by Tomas Horava goes over the bar.
6:07 Lukas Bajer produces a strike on goal direct from the free kick,
6:07 Sent off Tony Hibbert is shown a red card.
5:55 Free kick awarded for a foul by Tony Hibbert on Jakub Petr.
1:27 Shot by Tomas Janotka. Save by Tim Howard.
0:00 The referee gets the match started.
Live text and data provided by The Press Association.
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