Casey stood over a putt with the chance to win four times on the 18th green at Crans-sur-Sierre, Switzerland, three of them in the playoff.
But South African Lawrence made good on his first chance, pumping his arms when his birdie putt dropped to become the seventh three-time winner of this event, and the first since Spanish great Seve Ballesteros.
"I just fought so hard today," Lawrence said.
"I feel for Paul. He played great golf. It looked like it was his all day."
Englishman Casey holding a comfortable lead fell behind as Lawrence put on a dynamic charge. He regained the lead with a 15-foot birdie putt on the 15th, saved par with a 15-foot putt on the par-3 16th and came to the 18th with a one-shot lead.
And then the 49-year-old appeared to get an enormous break. His shot from the right rough came out heavy. It landed short of the stream and hit a rock that propelled it over the water and into deep rough.
But it was a nasty lie and he could only chip out to 20 feet. His par putt to win the tournament caught the left lip and he ended on 68 to join Lawrence on 18-under 262.
Casey had a 35-foot birdie putt for the win on the first playoff hole at No. 18. On the second extra hole, his 10-foot birdie narrowly missed to the right. Officials moved the pin toward the back of the green, and Casey had eight feet for birdie and the win. That spun off the right edge.
The fourth time around, Lawrence made the winning putt to capture the European Masters for the third time in the last five years.
"It's just the best feeling in the world," Lawrence said.
Harry Hall of England closed with a 63 and finished alone in third. Patrick Reed (66) tied for 11th, slightly expanding his lead over Rory McIlroy in the Race to Dubai.
