It is the 10th career complete game for Myers (8-6) and his first since May. He allowed four hits and struck out a career high-tying 12 batters.
Myers extended his club record for consecutive starts of at least six innings to begin a season to 21 with his performance.
"Wow. It's tough to separate them. You just can't," Mills said when asked if Tuesday's outing was Myers' most impressive this season.
Berkman's fifth career grand slam came in Houston's six-run seventh inning with the team leading 2-0. The slam, his first since Aug. 12, 2008, sailed over the bullpen and landed in the stands behind it in right-center field.
Berkman has struggled this season after having arthroscopic surgery on his left knee in March and is hitting .240. He said starting the season with the surgery has made things difficult.
"I think whenever you have a surgery right at the beginning of the season, miss all spring training and then try to come back two weeks in, you're always going to be a little bit behind," he said. "So I knew that coming in. I'd done it before and ... it's not the way you want to do it, but you can still be productive, particularly late in the season when you start to get your legs under you a little bit."
Myers retired the first nine batters he faced before giving up a double to Tyler Colvin to start the fourth inning. Myers walked Marlon Byrd with no outs in the fifth inning before retiring the next eight batters. Byrd singled with two outs in the seventh inning, but Alfonso Soriano grounded out to end that inning. Myers threw a perfect eighth inning.
He didn't allow a run until Colvin, a rookie, hit a solo homer to right field in the ninth. It was his 16th homer of the season. Myers gave up a single to Starlin Castro before striking out the next three batters to end the game.
Myers didn't want to reflect on if this game was his best this season.
"I don't try to look too much into it," he said. "We won. That's all I can really talk about. It was a good win for the team and we needed the win. I am happy that we all contributed."
Andrew Cashner (1-4) hit Humberto Quintero on the shoulder with a pitch with no outs in the seventh. Jason Bourgeois came in as a pinch runner, stole second base and advanced to third on a sacrifice bunt by Myers. Cashner intentionally walked Michael Bourn before Bourgeois scored on a bunt by Angel Sanchez when Cashner's throw to catcher Koyie Hill was a split second late to make it 1-0.
Houston pushed the lead to 2-0 when Hunter Pence drove in Bourn with a grounder to right field. Carlos Lee walked before Cashner hit Jeff Keppinger with a pitch to load the bases and set up Berkman's slam.
"I just didn't execute my pitches tonight, and it all started with Quintero," Cashner said. "I had him 0-2, could have put him away, and I hit him. It just kind of snowballed from there."
Cashner, who had been dealing with a sore throat but said he felt fine on Tuesday, allowed two hits and six runs in 1 1/3 innings.
Rookie Chris Johnson extended his career-best hitting streak to 11 games with a single in the second inning. His streak is the longest for a Houston rookie since Chris Burke had a streak of the same length in 2005. Johnson added a single in the fifth inning.
Cubs starter Ted Lilly allowed five hits and no runs with eight strikeouts in 5 2/3 innings. He was replaced by Cashner after walking Pence and Berkman in the sixth inning. Cashner struck out Johnson to end that inning.
"My stuff was better, my command, obviously that last inning I faltered a little bit," Lilly said. "I maybe was going a little bit too fast. But I am starting to feel like my stuff is starting to come around as we get along here a little bit."
Keppinger left Tuesday's game in the eighth inning with tightness in his lower back. ... C Geovany Soto was out of the lineup a day after leaving in the sixth inning after fouling a ball off his left foot earlier in the game. Cubs manager Lou Piniella said the bruised left foot was feeling better on Tuesday and that he was "50-50" to play on Wednesday. ... Mills said RHP pitcher Jeff Fulchino felt good on Tuesday after throwing one scoreless inning in his first rehabilitation appearance for Triple-A Round Rock on Monday. Fulchino, who is on the disabled list with right elbow tendinitis, will make another appearance on Wednesday. ... RHP Brian Moehler, who experienced tightness in his strained right hamstring while throwing a simulated game on Friday, is scheduled to throw off flat ground on Wednesday.