Jimenez pitched six effective innings, Tulowitzki hit a two-run double and the Rockies beat the San Diego Padres 4-2 on Sunday to take the deciding game in the first series of the season between the NL West rivals.
Colorado was coming off a 5-4 loss to the Padres in 14 innings on Saturday night in the longest game in the majors this season.
"Any time you play 14 innings and get a loss, usually a team comes out dead the next day," Tulowitzki said. "But I thought we responded nicely. We got on top of 'em early and held the lead late."
Jimenez (2-0) allowed two runs and seven hits. He also struck out seven while improving to 3-0 with a 3.15 ERA in his last three starts against San Diego dating to September 2008.
"I was hoping to go seven or eight innings, especially after last night's game," he said. "But I wasn't as sharp as I wanted to be. I was falling behind in the count. But I was still able to get through some innings using my fastball."
Franklin Morales got three outs for his second save in two chances, capping three innings of scoreless relief by the Rockies' bullpen.
"Our pitchers have done a huge job this whole series," Tulowitzki said. "Offensively, we're not where we need to be. Defensively, we're not where we need to be. We know we're a much better team and we need to pick up the intensity a little bit and start playing better. But any time you're playing a team in your division, it's nice to get a series win."
There was a downside for the Rockies, who lost center fielder and leadoff hitter Carlos Gonzalez to a tight left hamstring. Gonzalez was injured when he scored from second on Tulowitzki's double in the bottom of the third. Manager Jim Tracy said Gonzalez is day to day.
Gonzalez is off to a strong start. He tied his career high with four hits in the opener at Milwaukee and has an RBI or run scored in each of the Rockies' six games this season.
Jimenez stayed out of trouble until Chase Headley doubled with two out in the sixth to start a two-run burst. Will Venable followed with an RBI single and later came home on Yorvit Torrealba's infield single.
"You know any time you are facing Jimenez, you're in for a battle," San Diego manager Bud Black said. "Two runs at that time, you're still in the game, but you are in an uphill battle when you fall behind."
Jon Garland (0-2) went six innings for San Diego, yielding four runs and eight hits.
"I've left a lot of stuff out over the plate these early games," Garland said. "It would be good if I threw 95 mph or above, but I don't. I can't really get away with it."
The Rockies loaded the bases in the third when Jimenez reached on a fielder's choice, Gonzalez singled and Jason Giambi walked. Tulowitzki, 0 for 6 in a game for the first time in his career the night before, then doubled to center to score Jimenez and Gonzalez, who appeared to begin limping as he turned for home.
Miguel Olivo hit his second homer of the season in the fourth, putting the Rockies up 3-0 with a drive to center.
All three of the Rockies' wins this season have come in day games. ... Playing all 14 innings on Saturday earned Rockies 1B Todd Helton the day off. ... Jimenez has gone a franchise-record 55 regular-season starts in a row without allowing multiple homers. It also is the longest active streak in the majors. ... The Padres return to San Diego to play their home opener Monday against Atlanta.