Tulowitzki hit a game-ending RBI single that lifted the Rockies to a 6-5 victory over Milwaukee after the Brewers tied it with two unearned runs on Barmes' error in the ninth.
Center fielder Dexter Fowler, a defensive replacement in the eighth, initially kept the Brewers at bay when he leaped to rob Chris Dickerson of a homer leading off the ninth against Huston Street. Dickerson tipped his cap toward Fowler after the sensational catch.
But the Brewers loaded the bases with two outs after Street hit Rickie Weeks with a pitch. Second baseman Barmes then dropped Corey Hart's wind-driven popup, allowing two runs to score and denying Ubaldo Jimenez a club-record 18th victory this season.
"I thought it was over," Dickerson said. "The guys in the dugout saw [Barmes] struggling and said wait to see what happens. He's having trouble and he dropped it."
Barmes said the wind was no excuse.
"I should catch that ball 100 times out of 100," he said. "It's a pretty embarrassing play. More than that, it took the win away from Ubaldo. It's a hard pill to swallow. We did get the win, and thankfully I didn't lose the game completely."
Colorado responded in the bottom half against Trevor Hoffman (2-6), putting runners on first and second with two out. Tulowitzki then drove a Hoffman pitch back up the middle and past the glove of diving second baseman Rickie Weeks, scoring Fowler.
Jimenez struck out 10 in eight innings, allowing three runs and 10 hits, tying a season high.
"If you know Barmes, he's one of the best second basemen and if he doesn't catch that ball, I'm not sure someone else would have," said Jimenez, who remains tied with three other Colorado pitchers for the franchise record for wins in a single season. "I'm a human being. I wanted to win that game, but so what? We're going to have more opportunities."
Weeks had four hits for Milwaukee, matching his career high.
Ian Stewart homered in the fourth to give Colorado a 4-3 lead and Tulowitzki added his 12th of the season in the sixth.
The Brewers got to Jimenez for three runs on four consecutive hits in the third, starting with a triple by Weeks that sailed over the head of center fielder Carlos Gonzalez, who had taken a couple steps in before backpedaling.
Hart followed with an RBI single. He reached third on Braun's double and scored on Prince Fielder's two-run single to center. Jimenez then got Casey McGehee to ground into a double play and struck out Dickerson to end the inning.
Jimenez got some help from his defense in the fifth. With one out and runners on the corners, Jimenez struck out Fielder and Braun broke for second, drawing a throw from catcher Miguel Olivo as Weeks took off for home.
Shortstop Tulowitzki jumped to snared Olivo's high throw and fired the ball back home, allowing the catcher to make a sweeping tag that caught the back of Weeks jersey as he slid into home.
Milwaukee manager Ken Macha argued with umpire Mark Wegner that Weeks got a foot on the plate ahead of the tag, but the call stood.
Weeks has had five four-hit games in his career, including two this season. ... Jimenez has had 10 or more strikeouts in a game eight times, including a career-best 13 on May 3 at San Diego.