Cain failed to do that in the third inning when Colorado scored the game's only run.
Charlie Blackmon, the majors' leading hitter going in, led off the inning with a walk and took second on Brandon Barnes' infield single. After Blackmon and Barnes advanced on a double steal, Blackmon came home on Troy Tulowitzki's sacrifice fly.
"The double steal cost us a run there," Giants manager Bruce Bochy said. "(Cain) threw quality strikes. It was really (Colorado) taking advantage of mistakes we made."
The Rockies also got a big lift from their bullpen.
Tommy Kahnle and four relievers combined for two-hit ball over six innings after Brett Anderson was injured, leading Colorado to just its third win in the past 17 games at San Francisco's waterfront ballpark.
Kahnle (2-0) allowed one baserunner in two innings. Matt Belisle, Adam Ottavino, Rex Brothers and LaTroy Hawkins pitched an inning apiece to complete the three-hitter, with Hawkins finishing for his second save.
Rockies relievers extended their scoreless streak to 9? innings in this series.
A day after pitcher Madison Bumgarner hit a grand slam and drove in five runs, the Giants managed only three hits and were shut out for the first time this season.
San Francisco loaded the bases with two outs in the eighth but Brothers struck out Pablo Sandoval on five pitches to end the inning.
"With the bullpen we have, we can come in with any lead and hold the opponent (down)," Kahnle said.
Cain allowed four hits over seven innings with eight strikeouts and three walks. He is winless in his past seven starts at AT&T Park.
"I was throwing a lot of strikes and the ball was moving around quite a bit," Cain said. "But they got a leadoff walk and I did a bad job of keeping (Blackmon) on."
Tulowitzki went hitless in three at-bats in his return to Colorado's lineup after sitting out the series opener with a sore quad. Catcher Wilin Rosario was also back after resting a sore hand on Friday.
Even at full strength, the Rockies needed a big lift from their bullpen to pull this one out.
Anderson lasted just three innings after bruising the index finger on his left hand, apparently while grounding out to end the top of the fourth. Anderson took the mound to begin the bottom of the frame before a team trainer was summoned from the dugout.
"It felt like a firecracker went off in my glove," Anderson said. "I went out there and threw a warmup pitch and it felt like what I envision trying to throw with a foam finger feels like."
Anderson eventually walked off the field and was replaced by Kahnle.
Sandoval greeted the Rockies reliever with a double to the gap in left-center on Kahnle's first pitch after center fielder Blackmon missed on a diving attempt. After Buster Posey walked, Kahnle got Mike Morse to ground into a double play and struck out Hector Sanchez.
The Giants couldn't do much else, spoiling Cain's strongest outing of the season.
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