Poulter shot a 3-under-par 69 at the Olgiata Golf Club to finish with a 19-under-par total of 197. He fired a 61 Thursday to shatter a 34-year-old course record before persistent thunderstorms canceled play Friday, reducing the tournament to 54 holes.
Lawrie birdied the 17th to take a one-shot lead while Poulter three-putted from the back of the green for a bogey six, putting the Englishman behind for the first time all week.
After Lawrie pushed his drive out of bounds at the 18th, Poulter hit a perfect drive and hit a 9-iron to within four feet for a birdie.
"It was neck and neck all the way and it got very interesting towards the end. Unbelievable," said Poulter, who won the title two years ago. "Unfortunately for Paul he hit it out of bounds on the last. I don't think he even knew there was out of bounds over there.
"Then there was a little less pressure on my shot but I still wanted to make a three and it feels absolutely fantastic."