Phillips hit a two-run homer in the third, and Bruce added a solo drive leading off the fourth as the Reds overcame the departure of their 19-game winner after just eight pitches.
Phillips added an RBI single in the ninth for his third hit and the Reds scored another on a passed ball. This one takes some of the sting out of that short-lived 2010 run.
"I still see it now. They always show it on TV. They show me on TV making the last out, and it kind of [stinks]," Phillips said. "But honestly I'm glad it did happen."
Aroldis Chapman gave up a run in the ninth on a wild pitch but struck out Buster Posey with a 100 m.p.h. fastball to end it with runners on second and third.
San Francisco's Matt Cain allowed his first career postseason earned runs after going untouched during the Giants' improbable World Series season of 2010.
That same year, Cincinnati was swept out of the first round by the Phillies after getting no-hit by Halladay. This time, the Reds clobbered Cain and played on with poise when Cueto got hurt.
Cueto's status in the series is uncertain. Reds manager Dusty Baker said Homer Bailey would be his Game 3 starter, not Cueto.
"The pitch to Bruce wasn't too terrible but the hanging breaking ball to Phillips is just something that you don't want to happen in a big-game situation like this," Cain said.
Reds skipper Dusty Baker earned an emotional win in his return to AT&T Park for the playoffs 10 years after managing the Giants within six outs of a World Series title before losing to the wild-card Angels. He rejoined the team this week after an 11-game absence while recovering from a mini-stroke and irregular heartbeat.
In Game 2 late Sunday, righthander Bronson Arroyo (12-10) took the ball for the Reds against San Francisco lefty Madison Bumgarner (16-11).