The Cubs' offense, led by four home runs on the day, including two from Alfonso Soriano, spotted Gallagher a 6-0 lead after two innings.
Gallagher () threw 91 pitches, 60 strikes in the victory.
Cubs manager Lou Piniella called Gallagher's start "a positive outing."
"He was getting ahead of the hitters and even when he got behind, he was able to throw his breaking ball for strikes," Piniella told reporters. "It was a positive outing for him."
Piniella said Gallagher will start next Wednesday's game in Houston.
"It's pretty simple," Piniella said. "If you're pitching well and you're getting people out, you're going to get the ball. He had a real nice ball game, so next Wednesday he's got the ball in Houston."
Piniella said: "If he continues to pitch well, he'll stay right in the rotation. He's got a nice arm and he competes well, and right now he's pitching well."
In two starts with Chicago, Gallagher is 1-0 with a 4.35 ERA in 10 1/3 innings. According to the Cubs Media Relations Office, Gallagher is the fifth youngest Cubs pitcher to make his first start for the club in the last 10 years at 22 years and 133 days. Carlos Zambrano is the youngest at 20 years and 80 days (2001).
Gallagher was rated the No. 4 prospect in the Cubs' farm system by InsideTheIvy.com entering 2008.