Despite the shaky moments, Howell carded a two-under 68 to be on a 16-under total of 196 at a tournament he has led from the start.
The 39-year-old American will have his work cut out on Sunday as he goes for his first Tour win since 2007.
Lurking one stroke behind are Gore, who has not won on tour since 2005, and the rookie Champ, who is seeking his second win in a month.
Both shot 66 on the Seaside Course at Sea Island, with Gore's 17-foot eagle putt at the 15th slicing what had been a five-stroke lead to Howell back to one.
Webb Simpson, who eagled the 10th and had five birdies in a sparkling 63, was three behind Howell in a tie for fourth with Ryan Blaum (65).
Howell began the day with a three-stroke lead and appeared headed for another solid round after two early birdies.
But it threatened to unravel on the back nine as Gore began making his charge. Howell bogeyed 14 after driving into the rough to trim his lead to three strokes, and when Gore struck for eagle, the margin was one.
Howell recovered with a birdie at 15 but stumbled again with three putts at the 16th.
Champ, 23, made his seventh birdie at the 18th to join Gore in second and boost his hopes of another win after claiming the Sanderson Farms Championship three weeks ago.
Simpson enjoyed a bogey-free day.
"I knew I needed something low to have a chance," he said. "Tomorrow I am going to need a low round again and hopefully the rain holds off."
Zach Johnson also produced an eagle at the 15th to shoot 65 and was tied for seventh at 11-under in a group with Patrick Rodgers (61). (Reporting by Gene Cherry in Salvo, North Carolina; Editing by Ian Ransom)