"You never know who's going to step up," manager Charlie Manuel said. "This is a game of opportunity. When you get an opportunity, you have to take advantage of it. Some guys do and some guys don't."
The 23-year-old right-hander allowed one run and four hits while striking out seven and walking two, and he got all the support he needed.
Rollins hit solo shots batting left-handed off Ramon Ortiz in the sixth and from the right side against John Grabow in the eighth. It was the second time in his career that he went deep from both sides and his first multi-homer game this season. He has seven in his career.
Dempster (7-7) lasted just three innings, giving up six runs and seven hits. But what stood out to manager Mike Quade was one misadventure in the first inning.
Shortstop Starlin Castro waved off second baseman Darwin Barney on a pop fly by Michael Martinez with one out and lost the ball in the sun, allowing it to fall in for a single. That set the tone for a two-run inning and, really, a miserable afternoon for the Cubs.
"We've got to stop," Quade said. "Ball's in the sun, we've got to communicate. Cassie thought he had that all the way. I look back at this whole game to that play. The sun's been in the same damn spot for however long Wrigley Field's been here. ... Those are two talented kids in the middle of the diamond. We make enough mistakes, but it's so important for those guys to play well."
Martinez had two hits, two steals and scored two runs for Philadelphia. Chase Utley added two RBI doubles and scored one run. The Phillies broke this one open early.
With the game-time temperature at 97 degrees, they jumped on Dempster with two runs in the first, three in the second and another in the third.
That was plenty for Worley, who did not allow a hit until Geovany Soto singled with one out in the fifth. The pitcher also helped himself at the plate when he doubled with two out in the second to start that rally.
""I started getting a little tired," Worley said after throwing 111 pitches. "I think the heat was more tiring than the pitch count. I was fortunate to have a room down there that Cliff and Doc didn't have the last couple of days. They just finished it today."
Back-to-back two-out doubles in the second by Worley and Rollins along with a run-scoring single by Martinez and an RBI double by Utley made it 5-0. Brian Schneider doubled in a run in the third. Utley added another RBI double against Ortiz in the fourth, making it 7-0.
The Cubs scored in the seventh on Soto's fielder's choice grounder with the bases loaded, but the game was well out of hand by then.
For Dempster, it was a sharp contrast from his 2-1 win over Florida last week. He threw eight scoreless innings in that one, but this figured to be a difficult afternoon for him. Lefties came in with a .292 average, and the only right-handed hitter in the starting lineup was Worley.
"I felt like they'd get ahead and work the count, make me miss, and when I missed they didn't miss," he said.
A Ricketts family spokesman denied a report that chairman Tom Ricketts has talked to longtime baseball executive Pat Gillick. "While Tom respects Pat Gillick's Hall of Fame career, reports of a conversation are unfounded," spokesman Dennis Culloton said, adding there's been no contact between them. WSCR-AM in Chicago, citing major league sources, reported Wednesday that Ricketts and Gillick spoke as recently as last week, fueling speculation that the Cubs might be interested in hiring the newly elected Hall of Famer in some capacity. Ricketts was not available for comment. He gave general manager Jim Hendry a vote of confidence last month and said he's not interested in bringing someone in to oversee the baseball operation. ... Dempster's shortest start this season -- and in his career -- came at Arizona on April 28, when he gave up seven runs in one-third of an inning. ... The Phillies are 23-10 in day games.