Zambrano combined with two relievers on a four-hitter and Lee, who has the best batting average in the majors, had three more hits to lead the Cubs to a 4-0 win over San Diego on Sunday, their ninth win in 10 games.
The Cubs took three of four from the NL West-leading Padres -- including two shutouts -- and went 6-1 on a swing through Los Angeles and San Diego.
"Without a doubt, with all the adversity we had, I think people expected us to go the other way," Lee said. "We haven't. We've kept our heads up and we've been playing great baseball."
Lee went 3-for-5 with two doubles, an RBI and a run, raising his average to .385. Neifi Perez also went 3-for-5, extending his hitting streak to 14 games, and scored twice.
Lee had 16 hits on the seven-game trip and Perez had 14.
"Just keep it coming," manager Dusty Baker said.
"The key was for us to start swinging the bats," Lee said. "We weren't scoring runs. Now we're getting the pitchers the lead and they're holding it. That's good baseball."
The Padres fell to 1-4 in June after going 22-6 in May, a club record for wins in a month.
"We have to get back on track," manager Bruce Bochy said after the Padres lost a home series for the first time this season. "We need to win some ballgames."
Zambrano (4-3) pitched out of two jams and didn't allow an earned run for the third time in four starts. He allowed just three singles in seven innings, struck out seven and walked four. Will Ohman allowed a single in the eighth and Ryan Dempster pitched the ninth.
In his last start, Zambrano and two relievers combined on a one-hitter, but he didn't get the decision in a 2-1 win in 10 innings at Los Angeles on Tuesday night.
The Padres got runners to second and third with one out in the sixth, but Zambrano escaped trouble. Dave Roberts and Sean Burroughs opened with singles and advanced on Brian Giles' groundout to first. Zambrano then struck out Phil Nevin and got Ramon Hernandez to ground to shortstop.
Zambrano walked the first three batters in the first, but also got out of it unscathed.
Roberts drew a leadoff walk but was thrown out at second when Burroughs failed to execute a hit-and-run. Burroughs and Giles walked, but Zambrano retired Nevin on a popup and struck out Hernandez.
Zambrano said it took him a while to get into the game mentally, plus a bit of a threat from catcher Henry Blanco.
"Henry, he just told me if I don't throw a strike or anything like that, he will slap me. He told me I have to be more aggressive, and I looked like I was too calm out there."
Said Burnitz: "Zambrano's a beauty. He's such an intense guy. If he's not in the zone, he gets so mad at himself. His stuff is so dominating that when he's in the zone, he doesn't really get hit."
San Diego's Woody Williams (2-3) lost in his first start since May 1. He came off the disabled list and started in place of ace Jake Peavy, who has an upper respiratory infection.
Manager Bruce Bochy planned to limit Williams' pitches, and the right-hander came out after throwing 88 through five innings. He allowed one run on four hits, walked two and struck out one.
Williams gave up Patterson's two-out double in the fourth that scored Burnitz. With one out, Burnitz lifted a flyball to right-center, and started into a home run trot before seeing the ball hit off the base of the fence. When Burnitz pulled into second, he acted surprised that the ball didn't go out.
Lee hit a leadoff double to left-center opening the sixth off Chris Hammond and scored on Burnitz's single for a 2-0 lead.
The Cubs took a 3-0 lead in the seventh on Ramirez's bases-loaded infield single to shortstop Khalil Greene, who had a tough play.
- Several Padres still have upper respiratory infections. LF Ryan Klesko missed his second straight start. RF Brian Giles was still sick, but started.
- Peavy is scheduled to start Wednesday at home against Cleveland.
- The Cubs return home for a nine-game homestand that includes the first-ever regular-season matchup with the Boston Red Sox. The Cubs and Red Sox played in the 1918 World Series, which Boston won in six games.