"Jimmy told me, `Just get the win and let somebody get the save,"' Myers said. "I was like, `Whatever, just win the game.' It's kind of funny that he said that and then drove in the game-winning run."
Matt Murton's homer in the bottom of the eighth tied it at 1 for Chicago after Myers (9-6) held the Cubs scoreless on three hits through the first seven innings.
"He had good stuff and he had his control. He did a good job of mixing it up and keeping you off balance," Murton said.
Ryan Howard's 44th homer leading off the sixth had put the Phillies ahead 1-0.
Rollins then drove a double to right-center to score Nunez, and Thurston was thrown out at the plate on the play. Arthur Rhodes got the first out in the bottom of the ninth and Geoff Geary the final two batters for his first save in two chances.
"A walk, a bloop and a hit and that's the ballgame. That's a tough one to lose," Cubs manager Dusty Baker said.
"You never want to waste an effort like that," Rollins said of Myers' outing. "Tonight we were able to pull one out. That's playing winning baseball, doing what we can to win. No one trying to be the hero, just doing what they can."
Howard was in a 1-for-11 slide when he connected off Angel Guzman with a towering drive that easily cleared the fence in left-center for the game's first run.
"I don't want to walk the leadoff hitter. He beat me with my best pitch, the fastball," Guzman said.
Myers had been roughed up in his two previous starts, giving up seven hits and five runs in 5 2/3 innings against the Reds (a no-decision) and nine hits and six runs in 3 1/3 innings while losing to the Nationals.
But he was sharp from the outset against the Cubs and allowed just four hits in eight innings with one walk and nine strikeouts. The Phillies moved within 1¾ games of Cincinnati in the NL wild-card race.
"Right now it's been fun," Howard said. "We've been playing some good ball. We know what's at stake."
Myers walked leadoff hitter Juan Pierre -- he was thrown out trying to steal -- and then retired the next 10 batters before Aramis Ramirez doubled past third for Chicago's first hit with two outs in the fourth.
Freddie Bynum singled leading off the seventh for the Cubs' second hit, but was picked off first for the second out of the inning. Jacque Jones followed with a double into the ivy in right field, but Michael Barrett then flied out to end the threat.
"I got a little bit too anxious. That's all," Bynum said. "I was trying to get to second and get in scoring position but unfortunately he picked me off."
Guzman, making his sixth major league start, gave up just four hits in six innings with three walks and eight strikeouts.
Guzman struck out David Dellucci with the bases loaded to end the first after he yielded two walks and an infield single. The Phillies' next hit was Dellucci's two-out single in the fourth.
Rollins walked again with two outs in the fifth, moved up on a wild pitch and made third when Shane Victorino beat out his second infield hit of the game to short. However, Guzman struck out Chase Utley to end the threat.
- Howard was 1-for-18 in his career at Wrigley Field and 4-for-29 overall against the Cubs before his homer.
- Utley returned to the lineup after missing Tuesday's game with a sore ankle and leg as the result of his collision Monday with teammate Aaron Rowand, who broke his ankle on the play.
- Cubs C Barrett, out with a sore triceps, made his first start since Aug. 18.