With Pablo Sandoval on second and Randy Winn on first, Garko hit a line drive up the left-center field gap off Francisco Cordero (1-3). He finished with four RBI, as many as he had in his first 17 games after being acquired by San Francisco from Cleveland on July 27.
Garko admitted he might have been pressing since joining the Giants.
"My first time in the organization and being on a team in the race, I'm sure it's in the back of my mind," he said. "I don't think about it when I'm on the field, but I'm human. I'm sure it creeps into your head."
Juan Uribe added a sacrifice fly as the Giants sent the Reds to their fourth straight loss and fifth in the last six games.
The Giants' third win in four games allowed them to stay one game behind Colorado, which beat Washington 4-3, in the NL wild card.
Manager Bruce Bochy was happy to see the Giants rally and pick up Lincecum.
"That was one of our better [comebacks]," Bochy said. "That's an area where we haven't done too well."
Lincecum, who went into the game leading the majors with a 2.19 ERA, gave up as many earned runs in Cincinnati's four-run second inning as he had in his last four starts combined. The Reds batted around in the inning.
"We scored five off of Lincecum, and that's rare," Reds manager Dusty Baker said. "He didn't have his best stuff tonight. For him to walk in a run is rare. His velocity was down, too."
Reds starter Homer Bailey, 0 for 18 going into the game, followed with a two-run single down the first base line, his first hit and RBIs of the season. Bochy argued the ball was foul, vehemently enough to be ejected by first base umpire Marvin Hudson.
Chris Dickerson added an RBI single to make it 4-0 and give the Reds as many hits in the inning as Lincecum had allowed in his last game.
"I just wasn't myself tonight," Lincecum said. "I was trying to battle and keep us in the game."
Uribe hit his fifth homer of the season with one out in the third, but Joey Votto restored Cincinnati's four-run lead in the fifth with his 18th of the season and first in 51 at-bats since Aug. 2.
Votto's homer was the first off Lincecum in five starts since Atlanta's Yunel Escobar hit a three-run shot in the Braves' 4-2 win on July 22 -- Lincecum's last loss.
San Francisco tied the game in the sixth on Winn's two-run double with the bases loaded and Garko's two-run single.
"Garko can hit," Bochy said. "He had some good at-bats tonight. When he got here, he tried to do too much, but we'll throw him out there."
"It was good to come through with runners on base," Garko said. "I think it's important to have an approach with men on base."
Bailey left after walking the next batter. He was charged with five runs and seven hits in 5 2/3 innings.
"They're playing for the wild card," Bailey said of the Giants. "They're a good team. What can you say? In that inning, I was off by minute amounts. Nobody had any suggestions, including myself."
Lincecum, last season's Cy Young Award winner, finished with his third straight no-decision - his second such streak of the season. He allowed six hits and five runs with three walks and a season-low two strikeouts.
"It's fair to say he wasn't at the top of his game," Bochy said.
- Reds CF Willy Taveras left the game after seven innings with a right quadriceps strain.
- Bochy gave 2B Freddy Sanchez the day off to nurse his sore left shoulder. "It's kind of a day-to-day thing," Bochy said. "He said he wanted to play, but he needs a day. It's pretty sore."
- Bailey left tickets for tennis star and fellow Texas resident Andy Roddick, who is in Cincinnati for a tournament. Roddick, ranked fifth on the ATP Tour, sat in the first row behind the Reds dugout.