Jo (right) celebrates his opener with Pienaar at Goodison Park
Everton survived a brave fightback from Stoke to record a hard-fought win on the eve of David Moyes's seventh anniversary as boss at Goodison Park.
With the hosts utterly dominant early on, Jo's turn-and-finish was followed by a tap-in from Joleon Lescott to give them a comfortable lead at the break.
Ryan Shawcross headed in from a corner for Stoke and Glenn Whelan was inches from levelling for the visitors.
However, Marouane Fellaini's deflected injury-time goal sealed Everton's win.
It was a deserved victory in the end for the Toffees, but Stoke boss Tony Pulis will at least take comfort from a second-half performance that almost earned his side what would have been an important point in their battle against relegation.
As it was Everton were forced to rely on a measure of good fortune in repelling the visitors' fightback before Fellaini's last-gasp strike put a seal on their sixth win in seven games and ensured Stoke drop back down into the bottom three.
Moyes praises 'best-ever' squad
It was almost the archetypal game of two halves at Goodison Park, kicked off in impressive fashion by an Everton side clearly buoyed by their recent run of six matches without a defeat.
Steven Pienaar and Leighton Baines were at the heart of most of their good early play, terrorising Stoke down their right-hand side.
And it was that combination that created the first real chance of note, only for Leon Osman to blaze wide from 12 yards.
With Stoke happy to sit off the hosts in an attempt to keep things tight in and around their own box, Everton were able to play with plenty of verve.
And the opening goal was a fine example, the impressive Jo exchanging passes with Fellaini, turning past Shawcross into the box and firing under Thomas Sorensen and into the corner.
Six minutes later and it was 2-0 as Sorensen could only palm Tim Cahill's header tamely into the path of Lescott, who tapped in.
It might have been even more before half time had Osman kept his shot on target when he was 12 yards out, but the Toffees could hardly have been more comfortable as the half time whistle blew.
Stoke, though, have proved tough opposition in recent weeks and they upped their game after the break.
Everton did not help themselves by conceding a simple goal from a set-piece on 52 minutes, Shawcross heading home unmarked from Liam Lawrence's corner, but thereafter the hosts were forced totally onto the back foot by a resurgent Potters.
First Ricardo Fuller got behind the defence only to be denied by Lescott's saving tackle, and then Shawcross was inches away from turning Danny Higginbotham's header into an empty net.
Pulis regrets poor first half
Salif Diao and Whelan came even closer to equalisers with long-range efforts and Everton were hanging on grimly with 20 minutes to go.
But Everton rode the storm and finally began to reassert themselves in the closing stages, Jo almost putting the game beyond Stoke when only a smart, brave save at his feet from Sorensen denied him his second of the game.
With Stoke piling numbers forward in an attempt to repeat their feat of a fortnight ago when they came from 2-0 down to draw at Aston Villa, Everton always looked a danger on the break.
And so it proved two minutes into stoppage time when Fellaini pulled a long ball down in the box and his shot took a wicked deflection off Shawcross and into the net.
Everton manager David Moyes:
"It was a hard fought game, but we got the points just like we did in my first match here seven years ago against Fulham - that was a big day for me and I'm immensely proud to still be here seven years later.
"Steven Pienaar and Jo, in particular, were impressive and other parts of our game were very good too, so there were things to be pleased about other than the victory.
"We expected Stoke to come at us and after their goal they got some momentum, but we hung in, stuck at it and got the third late on to seal it.
"This is certainly the best squad of players I've had here in terms of attitude and application and I'll enjoy a celebratory drink this evening for sure."
Stoke boss Tony Pulis:
"We were very poor in the first half and it's happened too many times away from home this season that we've been slow out of the blocks and given ourselves a mountain to climb.
"But we were the better side in the second half and caused them all sorts of problems, which was encouraging.
"This league will ebb and flow as we go along but the important thing is we keep believing. We knew it'd be difficult today, Everton are a real forceful team, but we have to keep going and next week against Boro is now massive."
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