Marquis came within an out of the sixth complete game in his 10-year career and the Rockies beat Pittsburgh 7-3 Friday night for their 14th win in 15 games.
Manager Jim Tracy, who is 16-5 since taking over for Clint Hurdle on May 29, received a chorus of boos when he went to the mound following pinch-hitter Eric Hinske's run-scoring single with two outs in the ninth.
The fans gave Tracy a standing ovation when he spun around and returned to the dugout alone, having given Marquis one more chance at his second complete game of the season.
"He told me this was my last guy, it was make or break," Marquis said.
"I needed to make better pitches to Hinske and McCutchen. But you know what, we got the win and that's what matters," said Marquis (9-4), who allowed three runs on eight hits.
Marquis induced 21 ground-ball outs, three strikeouts and two flyouts, and he did it with not much working besides his wicked sinker.
"It's not the best I felt all year, but it was good enough to get the job done," Marquis said. "It's definitely fun when you get deep into games and watching guys make plays like that."
"He has the perfect left side of the infield with Tulowitzki and [third baseman Ian] Stewart," Pirates shortstop Jack Wilson said. "When you have Marquis throwing so well and those guys on the left side, its the perfect situation for the Rockies."
Marquis improved to 5-1 in his last seven starts, leading the Rockies' turnaround from an early-season funk.
Troy Tulowitzki and Hawpe each homered for the Rockies, who moved above .500 (34-33) for the first time since April 11.
"It's huge," Tulowitzki said. "I think it shows that we have a lot of talent. I mean, it's impressive because it got pretty bad. There's still a long way to go, but to be one game over .500, we've come a long way."
Tulowitzki fielded 10 groundballs at shortstop.
"He's fun to play behind," he said of Marquis, one of the league's top sinker-ball pitchers.
"It was frustrating," Pirates manager John Russell said. "We get shut down a lot. We have to find ways to bounce out of it."
Through the first five innings, Marquis surrendered just Freddy Sanchez's fluke single in the first inning. Nyjer Morgan took off from first base on the pitch and Sanchez hit a routine ground ball toward second baseman Clint Barmes that struck Morgan and dribbled into center field.
By rule, Morgan was called out for runner's interference and Sanchez was credited with a base hit.
That was all the Pirates mustered until McCutchen doubled leading off the sixth.
Pittsburgh right-hander Ross Ohlendorf (6-6) was tagged for six earned runs on nine hits in five fitful innings.
Wilson's second homer of the season made it 6-1 in the seventh.
Tulowitzki nearly hit another homer to center, this one off Matt Capps in the eighth, but McCutchen hauled it in at the wall, allowing Helton to score from third with his third run of the night.
Rockies setup man Manny Corpas received a cortisone shot and was shut down for the weekend in hopes he'll avoid a trip to the disabled list after an MRI discovered a floating bone chip in his right elbow. ... The Pirates designated OF Craig Monroe for assignment and recalled OF Steve Pearce from Triple-A Indianapolis. ... This was Tracy's first game against the Pirates, whom he managed in 2006-07.