Dexter Fowler had four hits -- three of them doubles -- and scored three runs, and Barmes finished with three hits and three RBIs for the Rockies, who won the final two games of the three-game series.
Tulowitzki, who replaced Barmes as the starting shortstop two years ago, has 23 homers, one short of his rookie season total. Barmes has a career-high 17 homers.
"That's 40 home runs for the middle infield, and oh-by-the-way gold-glove defense," Tracy said. "I think the only other tandem you can speak of in that vein would be the two guys that play over in Philadelphia. We have something special going on."
Tulowitzki, who has 18 homers since June 8, doesn't worry about the Rockies' defense being compared to other teams.
"What I know and what I'm happy with is we both care about defense and we're going to play the game the right way," he said. "Let everybody else decide if we're the best defensive duo."
Jimmy Rollins and Chase Utley have one thing their counterparts in Colorado want -- the World Series title the Phillies won last year. Barmes thinks this Rockies team, which leads the NL wild-card race by 1 1/2 games over San Francisco, can get back to the postseason.
"Hopefully this continues and keep playing into October," he said. "That's the No. 1 goal."
The Rockies' pitching staff will have a lot to do with that.
Marquis (13-8) showed the form that earned him an All-Star selection this year by becoming the third pitcher in the National League to reach 13 wins. He'd been 0-2 in his previous three starts, but gave up one run and struck out six with three walks Thursday.
"It's nice any time whether it's one, two, three or four, whatever number it is," Marquis said of his 13 wins. "I'm glad I got back on track. I still have work to do."
The right-hander got support early from his offense. Fowler led off the first with a double, moved to third on Barmes' single and scored on Todd Helton's double-play groundout. Tulowitzki followed with his 23rd homer of the season to make it 2-0.
The Rockies made it 3-0 when Fowler doubled in the third and scored on Barmes' single.
"To get some early runs, it made it a little easier," Marquis said.
The Pirates cut it to 3-1 on Andrew McCutchen's sacrifice fly in the fifth, but couldn't mount any more offense against Marquis. He ended his outing by getting catcher Jason Jaramillo to hit into an inning-ending double play on his 106th pitch.
"He pitched a good game, but when you get three hits you're not going to beat too many clubs," Pirates manager John Russell said.
The Rockies added another run in the sixth when Tulowitzki reached on a two-base error and came home on Garrett Atkins' single up the middle to make it 4-1.
Pittsburgh starter Paul Maholm (6-7) settled down in the middle innings before the Rockies put it away in the seventh. Ian Stewart, who led off with a double, scored when Jaramillo tried to pick off Fowler at first. Fowler went to third on the play and scored on Barmes' two-run homer, his 17th of the year.
Maholm allowed seven runs on 11 hits and struck out five in 6 1/3 innings.
"It's seemed every mistake was over the middle and they took advantage of it," Maholm said. "In the middle innings I felt a lot better. I was putting the ball where I wanted to and I was getting my breaking ball over for strikes."
The Rockies scored three more in the eighth on a two-run double by Carlos Gonzalez and a sacrifice fly by Stewart.
Fowler returned to the lineup after missing two games with a bruised left knee. Fowler injured the knee running into the center field wall making a catch in the ninth inning against the Cubs on Monday. ... Pittsburgh's Steve Pearce has reached base safely in nine straight games. ... The Pirates have not won a road series since taking three of four games from Washington on May 18-21.