Bryan LaHair hit a tying, two-run homer off Chad Qualls (1-0) in the eighth after Vance Worley threw seven impressive innings for Philadelphia.
But the Phillies answered in the bottom half. Scott Maine (0-1) hit pinch-hitter Juan Pierre with a one-out pitch and Jimmy Rollins singled off Rafael Dolis with two outs.
Polanco, who had just two RBIs in his first 71 at-bats, drove in two with a hard liner to the wall in left.
Jonathan Papelbon pitched the ninth for his eighth save in as many tries, giving Philadelphia a split of the four-game series.
The five-time defending NL East champion Phillies finished April at 11-12, their first losing record in a full month since going 11-15 in June 2009.
The bright side for the Phillies: They were only 12-10 in April 2010 and went on to win a major league-best 97 games.
Worley allowed one run and five hits, striking out five. He left with a 4-1 lead, but the bullpen blew it.
Antonio Bastardo started the eighth and got one out before walking Tony Campana. Qualls came in and allowed an RBI single to Starlin Castro after Campana stole second. LaHair then ripped a two-run shot to right-center for his fifth homer.
Worley lowered his ERA to 1.97, third-best among Philadelphia's starters. Roy Halladay's is 1.95 and Cliff Lee's is 1.96.
Often overlooked on a staff filled with aces, Worley was 11-3 as a rookie last season and has been even better this year. He's allowed two runs in 20 innings in his last three starts.
Cubs starter Chris Volstad gave up four runs - all in the first - and eight hits in six innings to remain winless since July 10, 2011. He is 0-8 in 16 starts since his last win when he was with the Marlins.
Rollins got the Phillies started with a drag bunt single leading off the first. After Shane Victorino reached on a one-out infield single, Hunter Pence hit an RBI single up the middle for a 1-0 lead. A two-out walk to Laynce Nix loaded the bases and Carlos Ruiz followed with a two-run single to right. Pete Orr's RBI single made it 4-0.
The Phillies helped Worley with nifty defense by shortstop Rollins and third baseman Polanco on consecutive plays in the third.
Worley pitched out of trouble in the fourth and fifth, leaving runners at second and third in both innings.
Another defensive gem by Polanco helped prevent a big inning in the seventh. The Cubs loaded the bases with no outs. Geovany Soto then hit a hard grounder down the line, but Polanco made a backhanded grab on an in-between hop, stepped on third and threw to first to complete the double play. A run scored to cut the deficit to 4-1.
NOTES: Lee will not be activated from the disabled list when he's eligible to come off Friday. He has been sidelined with a strained left oblique. He could return next week. ... An error by Soto at catcher snapped Chicago's four-game streak without one. ... The Cubs haven't won a series in Philadelphia since 2001 at the old Veterans Stadium. ... A crowd of 45,397 was the 230th consecutive sellout at Citizens Bank Park, including postseason games. ... Cole Hamels (3-1, 2.73 ERA) faces Brandon Beachy (2-1, 1.05) when the Phillies open a three-game series in Atlanta on Tuesday. ... Jeff Samardzija (2-1, 4.13) opposes Bronson Arroyo (1-0, 2.70) when the Cubs open a three-game set at Cincinnati on Tuesday.