A stroke in front at the start of another muggy day at the TPC Sawgrass, world number four Westwood trailed by two late in the day before regaining control with a two-under-par 70.
While Phil Mickelson and Tiger Woods began the round level before going in opposite directions, Westwood stayed in the hunt for his first PGA Tour victory in 12 years.
The Briton, regarded by many of his peers as the game's best player from tee to green, broke clear of a tightly bunched leaderboard with a birdie at the par-five 16th where he got up and down from left of the green.
He pushed his drive well right of the fairway on to a cart path on the last hole but, after getting a free drop, struck a superb approach over trees to 34 feet before two-putting for a 14-under total of 202.
"It was tough out there, the golf course changed a lot," he added after recording four birdies and two bogeys on a Sawgrass layout running fast and firm in breezy conditions.
Australian Robert Allenby was alone in second after firing a 67, with Americans Ben Crane (68) and US Open champion Lucas Glover (69), and Italian Francesco Molinari (71) tied for third at 12 under.
Slocum, who had been two ahead with six holes remaining, bogeyed 13 and 15 and then dumped his tee shot into water at the par-three 17th en route to an ugly five. He ended up with a 72 and a four-way tie for sixth at 11 under.
While Westwood is perfectly positioned to push on for his first PGA Tour title since the 1998 New Orleans Classic, Mickelson kept alive his hopes of replacing Woods as world number one this week. A distant nine strokes off the pace overnight, Mickelson charged into contention with a sizzling 66 to end the day five adrift.
Woods, again wayward off the tee, bogeyed the last two holes for a 71 to lie joint 45th at four under in the event considered the "fifth Major" by the players. "I need a lot of help but it doesn't look like that's going to be the case," Woods said.
