Wiebe, the second-round leader, needed to battle back down the stretch Sunday, and did so with a clutch, 12-foot birdie putt on the final regulation hole to end with a even-par 72.
He finished 54 holes tied with Pavin (69) at 11-under-par 205 under blustery conditions at Kapolei Golf Course.
After both players parred the first extra hole, Wiebe sank an 18-foot par putt on the second hole. Pavin's effort came up short, handing Wiebe his fifth Champions Tour victory.
Three-time major champion Vijay Singh registered a final-round 73 in his Champions Tour debut, ending in a tie for sixth at 8-under 208.
Swim Week Miami Beach 2014 [PHOTOS]