Ernst and Lynn each carded a 2-under 70 in the final round, finishing 72 holes knotted at 8-under-par 280.
The pair then replayed the 18th hole for the playoff.
Lynn encountered trouble when he drove into the rough, then put his second shot into a greenside bunker.
Ernst, meanwhile, gained the middle of the fairway with his drive and landed his approach shot within 14 feet of the hole.
Lynn got out of the bunker but couldn't make par, while Ernst wrapped up the win with two putts for par.
Third-round co-leader Phil Mickelson fell out of contention with bogeys on the 16th and 17th, carding a round round of 1-over 73 to end one shot off the pace at minus-7.