HOUSTON, April 5, 2014 (AFP) - Kuchar's effort included six birdies and two bogeys, and gave him a 15-under total of 201.
He was four strokes in front of overnight leader Sergio Garcia, who settled for a one-over 73 and was joined on 205 by Cameron Tringale, who posted a 69.
Australia's Matt Johnson was alone in fourth after a 71 for 207.
"It's a nice position to have played well last week, to have been in the last group with a chance to win and again to come back this week, completely different course and have another shot to win," said Kuchar, who carded a final-round 75 at the Texas Open last week and finished equal fourth.
Saturday's tee times were moved up and the players teed off in groups of three from both the first and 10th tees in order to get the round in before forecast storms moved into the area.
With the Masters, the first major championship of the year, due to start on Thursday at Augusta, Georgia, getting the $6.2 million (4.5m euros) completed on time takes on added importance.
Garcia started the day with a one-stroke lead over Kuchar, but that evaporated at the first hole where the Spaniard made bogey from a greenside bunker and Kuchar rolled in a six-foot birdie to go top.
Garcia pulled level with a birdie at the third, but Kuchar birdied the par-five fourth to reclaim the lead.
Kuchar added a 10-foot birdie at the fifth before a bogey at the ninth saw him make the turn one shot ahead of Garcia.
The American birdied three in a row from the 12th -- draining an 11-footer at 14 -- and was in firm control despite a bogey at the last.
"It's a bummer to three-putt the last one," Kuchar said. "My speed got a little off there ... but all-in-all I putted well.
"I'm not at all disappointed with the way I putted or the way I played."
Garcia had opened the back nine with back-to-back bogeys at 10 and 11. His second birdie of the day at the 12th proved to be the last he would find as Kuchar built a comfortable cushion.
Phil Mickelson, who will be gunning for a fourth Masters green jacket next week, fired a 72 to join a group on six-under 210.
Mickelson had been in doubt for the tournament after pulling his right oblique muscle and withdrawing in the third round of the Texas Open last week.
Former world number one Rory McIlroy, also playing with an eye toward Augusta, failed to find a spark as he cared a two-over 74 that left him tied for 37th.
"I just haven't been able to get anything going this week even though I feel like I am playing well," McIlroy said after a round that included four bogeys and two birdies.
"Every aspect of my game feels good and I'm driving the ball well while I also putted a little bit better today.
"It's just been one of those weeks where nothing is sort of happening out there and I just need a spark to get me going."
Leading third-round scores on Saturday in the US PGA Tour $6.2 million (4.5 million euros) Houston Open (USA unless noted, par-72):
201 - Matt Kuchar 66-67-68
205 - Cameron Tringale 68-68-69, Sergio Garcia (ESP) 67-65-73
207 - Matt Jones (AUS) 68-68-71
208 - Rickie Fowler 70-70-68, Ben Curtis 67-70-71
209 - Shawn Stefani 67-69-73
210 - Jon Curran 69-72-69, J.B. Holmes 66-73-71, Retief Goosen (RSA) 68-71-71, Phil Mickelson, 68-70-72
211 - Andres Romero (ARG) 72-69-70, Chris Stroud 68-72-71, Brice Garnett 68-71-72, Ryan Palmer 70-68-73
212 - Brian Gay 71-70-71, Charl Schwartzel (RSA) 67-75-70, Hunter Mahan 69-72-71, Martin Flores 68-72-72, Erik Compton 66-73-73, Jason Gore 67-71-74, Jim Renner 66-72-74
213 - Luke Donald (ENG) 71-71-71, Graham DeLaet (CAN) 70-71-72, Lee Westwood (ENG) 70-72-71, Camilo Villegas (COL) 67-73-7, Michael Putnam 68-72-73, Steve Stricker 68-69-76, Jimmy Walker 71-65-77