Six-time PGA Tour winner Kuchar put on a long game clinic and despite a closing three-putt bogey finished with a four-under-par 68 at the Golf Club of Houston.
The American started the day one shot behind Spaniard Garcia, who faded with a mediocre 73 to fall into a tie for second with American Cameron Tringale (69).
Kuchar has a six-shot gap on fourth-placed Matt Jones of Australia as he seeks a confidence-boosting victory heading to the Masters next week.
But he is mindful that he let one get away last week at the Texas Open, where he led halfway through the final round but could only tie for fourth.
"The game plan is to play four good rounds," Kuchar told PGATour.com after signing for a 15-under 201 total.
"It was nice to have a great week last week and have a chance to win, and to jump right back in the saddle and have a chance tomorrow, it's a good position to be in.
"It was another good performance. I feel like my swing's getting better and better. I played steady golf, made a couple of putts, but there weren't a lot of long ones."
World number 11 Kuchar did not sink a putt longer than 15 feet as he compiled six birdies and two bogeys.
He saved par from six feet at the 17th hole, but missed from a similar distance at the last to at least give his rivals a glimmer of hope.
Garcia, buoyed by a deft par-save after missing the green at the final hole, was encouraged that he at least remained within striking distance.
"I hung on well without playing my best," said Garcia, who is competing in Houston for just the second time.
"Obviously I didn't play as well as yesterday (65), which is difficult to match, but I didn't feel I played that badly, other than a couple of bad shots.
"Matt played really well under the conditions. It was still quite breezy and as firm as the greens were, it was difficult to hit it close."
Tringale has a holiday planned for next week, but will have to change his plans if he wins on Sunday and earns a last-minute spot in the Masters.
Due to bad weather forecast, officials moved up the final round tee times, with the leaders scheduled to start at 9:30 a.m. local time.
(Reporting by Andrew Both in Cary, North Carolina, Editing by Gene Cherry)