The Englishman is the highest-ranked player at the tournament on the Palm Beach Gardens course and he sits alongside a clutch of 11 players on even-par 70.
Westwood, along with the majority of players, struggled to deal with strong gusts of 20-30mph winds on Friday, but kept his cool to get home with a respectable score for the conditions.
World number three Luke Donald, the winner of last weekend's WGC-Accenture Match Play, did not fair quite as well as he shot a 73.
Meanwhile, American Levin hit four birdies and one bogey to finish one shot ahead of the field on three-under 67.
Afterwards, he said: "It's a different kind of golf. You get in a par mode, where you just have to take what the course gives you."
The 2009 Honda Classic champion Y.E. Yang, Stuart Appleby, Kyle Stanley, Greg Chalmers and Charl Schwartzel, all sit one shot behind Levin.
The adverse weather also resulted in play being suspended with 12 players still left on the course and they will complete their rounds early on Friday morning.