The game was delayed by rain in the seventh inning for 1 hour, 24 minutes.
Charlie Blackmon homered, and Chris Nelson had two hits and two RBIs in the Rockies' third straight win. Colorado needs two wins in its final seven games to avoid the franchise's first 100-loss season.
"We want to end on a good note and give us something to be hungry about in the offseason," outfielder Tyler Colvin said.
Pomeranz was considered the centerpiece of the deal that sent former 19-game winner Jimenez to the Indians in July 2011. He was 2-1 for Colorado late last season but has struggled this year.
Pomeranz (2-9) had been 0-6 with a 6.84 ERA since the All-Star break and had lasted past the fourth inning just once in his previous 10 starts.
He was happy to get through five innings for a chance at the win.
"I had a pretty good fourth inning so maybe that's why he let me go out there for a little longer," he said.
Pomeranz said a tweak in his delivery and a more relaxed approach helped him have more success. He induced 11 ground ball outs and consistently threw first-pitch strikes.
"In the starts before, I was trying to make too good of pitches. I tried to slow things down and keep it simple and throw strikes," he said. "Let them hit it, let them get themselves out instead of trying to throw the perfect pitch."
Pomeranz allowed three hits in his first win since July 6 against the Nationals.
"That was probably his best game since his start in Washington," Rockies manager Jim Tracy said.
The staff got plenty of support as Colorado reached double-digits in hits for the seventh straight game. Every starter reached base at least once as the Rockies piled up 10 hits.
"We have a bunch of young hitters, most of them have been up here for most of the year, and they're taking good at-bats," Colvin said.
Dave Sappelt had two hits for Chicago, which is winless in 15 road games against National League West opponents.
The Cubs loaded the bases in the second before Berken grounded out to end the inning.
Colorado added to its lead in the third. Blackmon led off with his second homer of the season, Nelson hit a bases-loaded, two-run single and Colvin scored on a double-play grounder by Andrew Brown to make it 6-0.
"Nelson had a terrific at-bat on the line drive to right field," Tracy said.
Berken allowed six runs and nine hits in four innings in his third start for the Cubs.
"The ball was up for the most part tonight," he said. "That's a recipe for disaster."
Chicago's best chance to score was thwarted by a great play by Nelson at third base. With runners at second and third and one out in the seventh, Sappelt hit a deep drive to left. Blackmon caught it at the wall and threw to Nelson at third, who made a sweeping tag on Joe Mather before Josh Vitters could score on the tag-up.
"I thought I could make it, but I shouldn't have gone," Mather said.
"It was just a bonehead play," Cubs manager Dale Sveum said. "Joe has got good instincts, and sometimes for whatever reason they just forget what the score is and the situation."
Cubs 2B Darwin Barney extended his errorless streak to 140 games. He needs one more game to tie for the major league record, set by Placido Polanco of the Detroit Tigers in 2007. ... The Rockies are trying to become the first team to hit .300 at home since 2007, when the Angels and Yankees did it. ... Colorado C Wilin Rosario was 0-for-4. It's the first time in six games he failed to get at least two hits.