Lehman's 3-under-par 69 was capped by a pressure, 4-foot birdie putt that came after Spittle had missed his own try for a birdie on No. 18, handing Lehman his third victory in as many years on the Champions Tour.
He claimed the crown with a 13-under 203, one stroke better than Sluman (67) and Spittle (70) at The Old Course at Broken Sound.
Lehman and Spittle had been chasing Sluman for the final three holes after Sluman had gone into the clubhouse with the lead at 12-under. Lehman birdied No. 16 and parred 17 while Spittle's birdie on No. 17 set up the final-hole showdown.
Olin Browne carded a 5-under 67, sharing fourth place with Russ Cochran (70) at 10-under 206.
Hale Irwin (71), Jim Rutledge (67) and first-round leader Jay Don Blake (70) were knotted one shot further back at minus-nine.
Swim Week Miami Beach 2014 [PHOTOS]