'Unbelievable,' said Poulter, who led wire-to-wire. 'I'm just so happy I hit a good drive on 18.'
Lawrie finished with a final-round 70, but it was his double-bogey on 18 that secured the title for Poulter. Poulter, who also won this event in 2000, earned his third career victory on the European Tour.
Heavy rain and thunderstorms washed out play on Friday causing the tournament to be shortened to 54 holes,
Poulter and Lawrie dueled the entire round Sunday at Olgiata Golf Club. Lawrie began the day one stroke behind Poulter, but birdied the first to tie for the lead. The duo remained tied through the fourth, as they each parred the next three holes.
Poulter reclaimed the lead with a five-foot birdie putt on five. Both men birdied the par-4 sixth, then each parred the seventh. Poulter rolled in a 12-footer for birdie on eight to extend his lead to two strokes over Lawrie, the 1999 British Open champion.
Ian Poulter talks about his win.
Lawrie came right back with a birdie at the par-5 ninth to get back within one shot. The pair each parred the 10th, before Poulter's lead grew back to two shots when Lawrie bogeyed the 11th.
The Scot got back within a stroke with a birdie on 12. After the duo parred the next two holes, Lawrie evened the match with a birdie on the par-5 15th.
Lawrie bogeyed the 16th, when his tee shot found a greenside bunker, to fall one behind. Poulter three-putted for bogey on 17, while Lawrie birdied the hole to take a one-stroke lead with one hole to play.
Poulter came through in the clutch with a birdie on the final hole when he stuck his second shot within five feet of the cup. Lawrie, needing only a par at worst to get into a playoff, faltered with a double-bogey after knocking his tee shot out of bounds.
'It was unfortunate that Paul hit his out of bounds but thankfully it was enough,' said Poulter. 'This is absolutely fantastic because I hadn't won this year and I've made it my goal to win every year on tour. I've done that throughout my pro career and this keeps me going forward and bettering myself all the time.'
Lawrie was looking for his seventh European Tour win and second this year. Earlier this season, Lawrie won the Wales Open.
'I would have bet my house on making four up the last,' said Lawrie. 'I thought I hit a pretty good swing on the last and it came off at an unbelievable angle right.'
Anthony Wall, Anders Hansen and Emanuele Canonica tied for third at 15-under-par 201. Barry Lane, Angel Cabrera, Jarrod Moseley and Padraig Harrington were one stroke further back at minus-14.
Nick O'Hern also carded a final-round 63 to finish at 13-under 203. He was joined there by Stephen Gallacher and Henrik Nystrom. Philip Golding, who also shot 63 on Sunday, and Andrew Marshall were one stroke back at minus-12.
Final scores from the Italian Open