A leaping grab against the left-field wall by Andres Torres on a long drive by Reds catcher Ramon Hernandez to begin the ninth inning helped seal the victory and preserve the 15th save for Giants closer Brian Wilson.
"In tough situations, guys came in and made the pitches they needed," said Wilson. "We have the mentality that we're going to come at you with our best stuff. We're not going to pitch around people."
The bullpen's efforts backed starter Barry Zito, who allowed five runs and eight hits in 5 2/3 innings.
Zito, who was 3-2 with a 7.13 ERA in seven previous starts against Cincinnati, including a 6.28 ERA at Great American Ball Park, walked three and struck out four in a 96-pitch effort.
"I had decent stuff," Zito said. "I left a couple curveballs up. It's a different ballpark here. There are a few parks in this league that are a challenge to pitch in."
Zito helped his cause with an opposite-field, two-run single in the second off Reds starter Johnny Cueto, which put the Giants ahead, 2-0.
Cueto allowed four runs on 10 hits in six innings. He walked one and fanned five.
San Francisco led 4-1 following a two-run single by Uribe in the third.
The Giants made a bid to increase their lead in the fourth, but Buster Posey was thrown out at the plate attempting to score on Torres' single to center.
Posey's second-inning single extended his hitting streak to six games. Freddy Sanchez now has hit in 11 straight after his third-inning hit.
Zito had good rhythm with Posey, who was making his first start this season behind the plate, throughout Monday's outing.
"Buster was great," Zito said. "We were on the same page all night. I pretty much stick to my game plan. But it was pretty seamless with us tonight."
The Reds, who own 19 come-from-behind victories and 11 wins in their last at-bat, rallied back in the fourth.
Scott Rolen tripled and scored on Jonny Gomes' sacrifice fly to make the score 4-2.
Jay Bruce followed with his eighth home run, a solo shot to right that trimmed the Giants' lead to one.
"I have to tip my cap on the Bruce home run," Zito said. "I was trying to throw a strike there on 1-1."
The Giants loaded the bases with one out in the sixth. But Cueto fanned Zito and got Torres to fly out to center fielder Drew Stubbs, who made the catch one step from the wall.
Zito issued consecutive walks to load the bases with two outs in the sixth.
"He pitched himself into trouble," said Bochy.
Pinch-hitter Miguel Cairo's single to left drove home two runs to put the Reds ahead, 5-4, ending Zito's night.
"I left a couple curveballs up," Zito said. "[Cairo] has got to respect the fastball. Bottom line, if I make the pitch, it's probably a better result. I got it up in the zone."
Uribe's two-run single gave San Francisco a 6-5 lead it would not relinquish.
But Monday's game was a nail-biter into the ninth when Torres made the defensive play of the evening on Hernandez's long drive.
"I thought it wouldn't be catchable for a minute there," Torres said. "He got some good backspin on that ball. That's why I jumped."
Daniel Ray Herrera (0-3) took the loss for Cincinnati.
Sergio Romo (2-3) pitched two-thirds of an inning to earn his second win for the Giants.
"In any bullpen, when you have an idea when people are going to throw, it makes it easier," Wilson said. "We've molded into our roles. It's an advantage."