Coulthard clocked a 1minute 25.796seconds lap, almost three-quarters of a second adrift of Ferrari driver Rubens Barrichello, who topped the standings with his first run time of 1:25.057.
The Scottish McLaren driver spun out of second free practice on Friday after just over 10 minutes of the hour-long session.
Coulthard lost the rear of his McLaren-Mercedes MP4-15 at the second Lesmo bend and careered through the gravel trap.
He stopped, just before hitting the tyre wall, to the cheers of the tifosi, the enthusiastic Italian Ferrari fans for whom the trip to the Monza track for this race is equivalent to a pilgrimage.
Coulthard said that the spin was caused by a suspension failure on his McLaren.
Hopes alive
The 29-year-old, who trails his McLaren team-mate by 13 points and has already stated he must win Sunday's Italian Grand Prix to keep his Formula One world title hopes alive, was forced to settle for the fifth quickest time of the day.
His spin will have limited the amount of time he could devote to setting up his car, which can upset a driver's preparation for a Grand Prix weekend.
In this instance, though, Coulthard is unlikely to suffer too much - the teams had three days of comprehensive testing at Monza last week to prepare for the race.
"Despite today's incident I'm not too worried," he said. "What happened was unfortunate, but thankfully there was no damage to the car.
"We just need to dust it down, fit a new rear suspension and go for it tomorrow. I feel quite relaxed about the whole weekend and I'm tuned in to what I have to do.
Good qualifying
"It's pretty straightforward - just have a good qualifying and a good race. I know I can do it. It's just a question of everything going my way.
"And as long as I keep Mika and Michael [Schumacher] behind me then the championship is still on, but you don't have to be a brain surgeon to work that out."
Coulthard clocked a 1minute 25.796seconds lap, almost three-quarters of a second adrift of Ferrari driver Rubens Barrichello, who topped the standings with his first run time of 1:25.057.
Michael Schumacher was just 0.06s behind his Ferrari team-mate. The Jordan of Jarno Trulli finished third, with Hakkinen fourth. 0.5s down.
Ferrari's performance will be a psychological boost for the home team, for which this is also a crucial race.
Struggle
Schumacher trails Hakkinen by six points in the championship after the Finn won three of the last four races.
Ferrari had appeared to struggle in last week's test, but Schumacher has said that he believes aerodynamic improvements to his car for the race should help the team get back on terms with McLaren.
But times from Friday's practice sessions are a notoriously unreliable indicator of form, as the teams use differing fuel loads and some also fit new tyres. These can make huge differences to performance.
Briton Eddie Irvine showed the most improvement in the second hour as he moved up to sixth from 17th in his Jaguar, recording a time of 1:25.907, with team-mate Johnny Herbert down in 12th.
Jenson Button, who qualified third and finished fifth at the Belgian GP two weeks ago, was 11th with a time of 1:26.452. Coulthard, Button, Irvine, Herbert and Schumacher were just a few of the notable names to miss the turn into the revamped first chicane, which was continuing to prove a major headache.
They were all forced onto the run-off area of the Prima Variante before eventually returning to the track after negotiating a series of bollards.
Stop-go penalty
With the drivers facing a 10-second stop-go penalty for such an infringement in the race proper, this was the opportunity to iron out any mistakes.
Meanwhile, the inquest into the deaths of the two pilots that died when the plane Coulthard was travelling in crashed at Lyon Satolas airport on May 2 began at Leamington Spa on Friday.
David Saunders and Dan Worley died on impact, but Coulthard, fiancee Heidi Wichlinski and personal trainer Andy Matthews all scrambled from the wreckage.
Italian GP, Monza, Friday's Free Practice Times
1 R Barrichello (Bra, Ferrari) 1min 25.057secs
2 M Schumacher (Ger, Ferrari) at 0.060secs
3 J Trulli (Ita, Jordan) at 0.333
4 M Hakkinen (Fin, McLaren) at 0.496
5 D Coulthard (Gbr, McLaren) at 0.739
6 E Irvine (Gbr, Jaguar) at 0.850
7 P de la Rosa (Spa, Arrows) at 0.855
8 P Diniz (Bra, Sauber) at 0.924
9 J Verstappen (Ned, Arrows) at 0.963
10 M Salo (Fin, Sauber) at 1.236
11 J Button (Gbr, Williams) at 1.395
12 J Herbert (Gbr, Jaguar) at 1.577
13 M Gene (Spa, Minardi) at 1.581
14 H-H Frentzen (Ger, Jordan) at 1.706
15 G Fisichella (Ita, Benetton) at 1.752
16 J Villeneuve (Can, BAR) at 1.849
17 R Zonta (Bra, BAR) at 2.013
18 A Wurz (Aut, Benetton) at 2.036
19 N Heidfeld (Ger, Prost) at 2.078
20 G Mazzacane (Arg, Minardi) at 2.411
21 R Schumacher (Ger, Williams) at 2.795
22 J Alesi (Fra, Prost) at 2.847.
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