Taveras strolled to first base with the decisive RBI after sprinting toward the gap for a diving catch, and the Rockies kept on racing toward the World Series.
"We realize there's more work to be done," Todd Helton said. "Denver is going to be a crazy place this weekend."
Two wins at Coors Field would give Colorado the first pennant of its 15-season history.
"We're playing with a lot of momentum," manager Clint Hurdle said.
The Rockies recovered after blowing a ninth-inning lead with help from Taveras, playing his second game since missing 24 with a leg injury.
Leading off the 11th, pinch-hitter Ryan Spilborghs reached on an infield single. Brad Hawpe walked with one out and Jamey Carroll walked with two outs against Valverde, pitching more than an inning for just the second time this season.
"Until he gives up a run, it's his game," Diamondbacks manager Bob Melvin said.
But Valverde couldn't find the plate against Taveras, either.
"I felt so good. I'm not tired. My arm felt good," said Valverde, who threw 42 pitches. "That's my first time throwing that many pitches."
The wild-card Rockies, who swept Philadelphia in the division series, joined the 1976 Cincinnati Reds as the only NL teams to win their first five games in a postseason.
"We expect to win every game," Spilborghs said. "To come out of here with two wins is pretty much what we expected."
The Diamondbacks tried almost everything to come back, sending sweet-swinging pitcher Micah Owings to the plate as a pinch-hitter in the 11th.
Owings had 12 hits in his prior 21 at-bats, with three homers and 10 RBI. But he flied to center for the second out and Ryan Speier fanned Chris Young to complete a perfect inning for his first major league save in a game that lasted four hours, 26 minutes.
"We've come back from some difficult circumstances this year," Melvin said. "It's two games. A team has to win four before it's over."
His backhand flip to second was high for an error, and slick-fielding shortstop Troy Tulowitzki came off the bag to grab it.
Drew, however, didn't realize he was called safe by umpire Tom Hallion and wandered off second base. Tulowitzki, who had started to argue, soon noticed. He ran toward Drew and threw to third baseman Carroll, who applied the tag.
"From my standpoint, it looked like he touched it," Drew said. "When I looked back, there was no call. I thought I was out. That's it."
It was a costly mistake by Drew, in his first full season in the majors. Tony Clark grounded out, ending the inning.
"He just assumed he was out. He took his eye off the umpire and was coming off the field," Melvin said. "He didn't see where Tulowitzki was."
It was Corpas' second blown save since becoming Colorado's closer in midseason. The first was Sept. 21 at San Diego. He saved all three playoff victories over Philadelphia.
Left off the first-round roster, the speedy Taveras put the Rockies ahead 2-1 in the fifth when he scored on Helton's sacrifice fly.
With the Rockies clinging to that one-run lead in the seventh, Taveras' speed was a huge factor again. The Diamondbacks had a runner on first with two outs when Clark hit a drive to right-center off LaTroy Hawkins.
Taveras raced into the gap and laid out with a fully extended dive to make an outstanding grab.
"I don't know how many other guys in the league can make that play," Hurdle said.
The Rockies won their previous seven games wearing black jerseys, but they had to settle for gray with pinstripes in this one. The Diamondbacks broke out the black, something they had reserved for home Saturday night games in the regular season.
The styles of the starting pitchers could hardly have been more different. Colorado rookie Ubaldo Jimenez regularly hit 99 mph on the Chase Field radar gun. Davis uses a stop-and-go motion and an array of breaking pitches.
Davis, who had four hits in 58 at-bats all season, doubled leading off the third for his first extra-base hit since 2005. He scored when Young singled up the middle on a 98 mph pitch to tie it at 1.
After Mark Reynolds' error on Helton's grounder to third in the second inning, Davis struck out consecutive batters before Hawpe singled and Yorvit Torrealba hit a bloop single that put the Rockies in front.
In yet another demonstration of the way things are going for Colorado, Torrealba's opposite-field hit landed on the right-field line.
Missed opportunities abounded for Arizona.
The Diamondbacks loaded the bases in the fifth, but Reynolds struck out. Clark led off the second with a double that Taveras had in his glove as he ran toward the 407-foot sign in center before the ball popped loose. Still, Arizona failed to score.
The Rockies are up 2-0 despite a .211 batting average and 22 strikeouts. They have won 10 straight road games.
"We're fundamentally sound, we pitch better, we find ways to win," Hurdle said.
- It was the second extra-inning victory in the Rockies' 19-1 run.
- The big screen at Chase Field shows a clip of the season's highlights, and the ballpark echoes with boos every time Barry Bonds is shown hitting his record-breaking home run.
- Arizona reliever Tony Pena struck out the side in the seventh, giving him six consecutive strikeouts in the series.
- Valverde walked three in a game for the first time since April 24, 2004.