Garcia, a non-roster invitee in Padres camp, is competing for a spot in the rotation and made a statement with his start.
"We've seen the success of the secondary pitches down below the strike zone with a lot of action," Padres manager Bud Black said of Garcia. "It's a deceptive arm speed that can create a lack of timing for the hitters.
"[Tonight] he got ahead and put them away."
Garcia entered Tuesday's game with a spring ERA of 13.50 as he had previously allowed 10 runs over 6 2/3 innings.
Against the Giants, Garcia was a different pitcher. The right-hander struck out six over four innings and allowed one run on three hits.
Offensively, Mark Kotsay continued to hit at a torrid place. The veteran outfielder entered Tuesday's game hitting .600 with three RBIs this spring and added an RBI triple on a 1-for-2 night.
Everth Cabrera also had a good game for the Padres, going 3-for-4 with a stolen base.
Sandoval returned to the Giants on Tuesday after Venezuela recently was eliminated from the World Baseball Classic and Lincecum was pitching after a blister caused him to skip two scheduled starts.
"Thought he did pretty good," Giants manager Bruce Bochy said of Lincecum. "Overall I thought he did a good job, had good stuff with all his pitches."
Lincecum allowed three runs in 2 1/3 innings.
"Tonight wasn't good for a lot of us," Bochy said. "It was an off night."
San Francisco got on the scoreboard when Johnny Monell hit a solo home run, his first of the spring, in the third inning to right field.
Up next for Padres: Projected Opening Day starting pitcher Clayton Richard gets the start at 1:05 p.m. PT Wednesday against the Angels at the Peoria Sports Complex on MLB.TV. Richard is scheduled to go four or five innings. His last start was cut short by rain against the White Sox on Friday. He threw three innings in that game, though the statistics don't count. Officially, Richard has appeared in one game and has thrown just two innings. The Padres didn't use him in games early in Arizona because of a longer Spring Training and they felt no need to have him appear in games in February.