In between the Cubs benefited from two bloop hits, one Paul Konerko error, one Jose Valentin misplay and plenty of feistiness against three White Sox pitchers.
"We didn't hit the ball hard," Cubs manager Don Baylor said, "but they were placed in the right spots."
Baylor had a rare chance to beam after this one.
The manager will send Kerry Wood to the mound Sunday to try to complete the Cubs' first series sweep of the season.
Heck, Saturday marked just the third time all season the Cubs won the first two games of a series.
They trailed 2-0 after Valentin's two-out double off Jon Lieber in the fifth. That scored Ray Durham and left-hander Mark Buehrle, who had recorded his first major-league hit on an 0-2 pitch.
The Cubs rebounded with two in the bottom of the inning. With runners at second and third, Darren Lewis survived an eight-pitch at-bat by fouling off several pitches. He finally stroked a single to left field on a 2-2 fastball.
"It's not too often they can make perfect pitches every time," Baylor said. "If you keep fouling them off, you might get one you can hit."
Said Lewis: "I probably swung at some bad pitches. But he throws a lot of pitches inside so you have to be aggressive."
After catcher Mark Johnson put the Sox back on top in the sixth with his second homer of the season, the Cubs tortured Buehrle with soft singles.
Todd Hundley followed Alou's leadoff double with an opposite-field single.
With runners at first and third, Alex Gonzalez hit a two-hopper to Valentin at third. Instead of going for the double play, Valentin tried to tag Alou, who was leaning off third. That attempt failed, and the bases were loaded.
Chris Stynes, an accomplished pinch-hitter with just an .083 average at Wrigley this season, stepped to the plate.
Sox manager Jerry Manuel stuck with Buehrle even though Stynes was 3-for-3 against him in his career.
"We felt he was our best shot," said Manuel, aware of the numbers.
Stynes fisted a 2-2 fastball into left field to score two runs and give the Cubs a 4-3 lead.
Then Corey Patterson, replacing Lewis, hit a seemingly innocuous two-hopper to first. Konerko booted the ball, prompting sarcastic chants of "Paul-ie! Paul-ie!" from the crowd.
"I got a bad first step," Konerko said. "Then it was textbook letting the ball play you."
After Mark Bellhorn struck out, Sammy Sosa came through with a two-run double. It came on Rocky Biddle's superb pitch, an 0-2 breaking ball that shattered Sosa's bat before the ball found a home down the right-field line.
Patterson flew home from first to give the Cubs a four-run lead.
"When you get those two-out hits, it always seems like someone's on base," Baylor said.
Or at least that's how Baylor remembers it. His team entered the game batting .180 with two outs and runners in scoring position.
After Lieber departed, Juan Cruz and Antonio Alfonseca preserved the victory for the Cubs with three shutout innings.
"You want to finish things," Lieber said, "but if we can get to the sixth or seventh, we know that those guys can shut the door."