Cook seemed on his way to victory, holding a two-stroke advantage at the start of the 18th hole. But he botched his approach shot, putting it into the water hazard. After his drop, Cook placed his fourth shot to within 18 feet of the pin with a chance to win.
But he couldn't hole his next putt and Blake, who he had rolled in an eight-foot birdie to finish at 9-under par 204, forced a playoff.
Cook recovered on the extra hole -- also on the 18th -- pouring in a birdie putt to make up for his earlier error. He collected his seventh career Champions Tour win and second this season.
Cook carded a 2-over 73 while Blake notched a 1-under 70 at the TPC Tampa Bay.
Russ Cochran closed with a double-bogey to end at 3-over 74, tied for third with Joe Ozaki (68) at seven-under 206.