SAN ANTONIO, 28 Mar 2015 (AFP) - Walker, who lives just a half-hour's drive from TPC San Antonio, had a 54-hole total of nine-under-par 207 and a comfortable cushion over rising US star Jordan Spieth.
Spieth, the 21-year-old who also hails from Texas, carded a one-under 71 for 211.
He was two strokes in front of last season's FedEx Cup playoff champion Billy Horschel, who birdied the last three holes in a 71 for 213.
Walker, who captured his fourth PGA Tour title at the Sony Open in Hawaii this year, started the day with a one-shot lead over Charley Hoffman and Aaron Baddeley.
He closed his round with back-to-back birdies, chipping to seven feet at 17 and draining a 10-footer at the last, and was pleased with his effort on another tough, windy day.
"It was a tough day today. It blew really hard again,out of the south today. So I know it's a windy golf course, but it's still tough," Walker said.
"The greens are firm. You can see some spots starting to brown out a bit."
Spieth, who started the day two shots adrift, gained ground with four birdies in a five-hole span on the front nine and was tied for the lead through 13 holes.
But he played the final five holes in one over par with a bogey at 14 followed by a birdie at 15, double bogey at the par-three 16th and birdie at 17 before he capped his round with a par at the last.
"I just kind of let some get away from me there," Spieth said.
"I didn't play the smartest shots and was being a little too aggressive for this golf course."
Scott Pinckney carded a 69 to vault into a share of fourth place on 214.
He was tied with former Masters champion Zach Johnson (72), Brendan Steele (72), Jason Kokrak (71) and Chesson Hadley (71).
Australia's Baddeley had a disastrous day, his seven bogeys including four in a row on the front nine on his way to a four-over 76 that left him on 215, alongside Chris Kirk and Kevin Na.
Hoffman, who had led after the first round with a bogey free round in tough winds, fared even worse -- signing for a 79 that left him 11 adrift on 218.
Leading third-round scores on Saturday in the US PGA Tour $6.2 million Texas Open (USA unless noted, par-72):
207 - Jimmy Walker 71-67-69
211 - Jordan Spieth 71-69-71
213 - Billy Horschel 72-70-71
214 - Scott Pinckney 73-72-69, Chesson Hadley 71-72-71, Jason Kokrak 72-71-71, Zach Johnson 71-71-72, Brendan Steele 74-68-72
215 - Chris Kirk 71-71-73, Kevin Na 72-68-75, Aaron Baddeley (AUS) 68-71-76
216 - Carlos Ortiz (MEX) 79-67-70, Matt Jones (AUS) 77-71-68, John Merrick 72-72-72, Daniel Summerhays 71-73-72, Phil Mickelson 70-72-74
217 - Fabian Gomez (ARG) 72-74-71
218 - Bryce Molder 73-74-71, Scott Piercy 72-76-70, K.J. Choi (KOR) 75-70-73, Ryan Palmer 70-75-73, Pat Perez 78-71-69, Brendon Todd 73-70-75, Gary Woodland 75-75-68, Dustin Johnson 78-72-68, Charley Hoffman 67-72-79
219 - Kevin Chappell 73-73-73, Michael Thompson 73-73-73, Luke Guthrie 76-73-70, John Huh 73-72-74, George McNeill 74-70-75, Jeff Overton 75-70-74