"The two home runs were really the only two mistakes I made," Maholm said. "The first one, the fastball ran back over [the plate], and the second one was a hanging curveball. He did a good job, obviously, hitting them a long way."
Maholm, who had won his last five decisions for the Cubs while posting a 1.00 ERA, recorded a quality start despite the two mistakes to Maxwell.
The left-hander allowed just four other hits over his seven innings and struck out eight while walking two. But his record fell to 9-7.
"Most nights with our offense, we win that game," said Braves manager Fredi Gonzalez, whose team was held to four hits by Lucas Harrell and the Astros' bullpen.
The victory snapped a 10-game road losing streak for Houston and was just the Astros' fourth win in their past 33 games.
The loss, meanwhile, was only the Braves' eighth in their past 28 games as they fell to three games behind the Nationals in the National League East. They can complete an 8-2 homestand with a victory over the Astros on Sunday in the series finale.
Still, they were hoping for even more. Everything seemed set up perfectly for the Braves in Maholm's debut, as the left-hander had been 3-0 with a 1.62 ERA in his past five starts against the Astros.
The Braves first targeted the Cubs' Ryan Dempster in their search of a starting pitcher, but the veteran right-hander nixed that deal. So general manager Frank Wren acquired Maholm along with outfielder Reed Johnson.
Maholm grew up a Braves fan in Mississippi, and he used to come to Turner Field as a fan. Who could blame him if he was a little hyped up, but he said he wasn't.
"I was good," he said.
Maholm faced one over the minimum in the first three innings thanks to a double play and a caught stealing. But the Astros took a 2-0 lead in the fourth.
Maxwell lined a 1-0 pitch into the left-field seats with Ben Francisco on base after a single. Maholm had allowed just one homer over 45 innings in his last seven outings with the Cubs.
The Braves tied it in the sixth on Dan Uggla's two-run single, but then Maxwell struck again. Maholm hung a breaking ball on an 0-1 pitch and the right-handed hitter didn't miss it, sending another no-doubter into the left-field seats.
"That big breaking ball to Maxwell blew right into his wheelhouse," Gonzalez said.
"I don't know how far it went, but I took a pretty good swing," said Maxwell, who finished with the first four-hit game of his career. "We were watching on the bench. After I hit my first one on a fastball, he started throwing more curveballs, so that's what I was looking for."
It looked like the Braves might break through early against rookie right-hander Harrell (9-7). Jason Heyward doubled and Chipper Jones walked with two outs in the first inning, but Freddie Freeman lined out to left field.
Harrell then seemed to settle in until losing his control in the sixth. He walked the bases loaded and Uggla singled with two outs to tie the game.
"I've been feeling a lot better," said Uggla, who may be ready to break out after a long slump. "It's not quite right yet. When I get hot, I can get as hot as anyone."
Harrell had helped stop Houston's record 12-game losing streak in his previous start against Pittsburgh on July 29, and has now allowed two or fewer earned runs in five consecutive starts.
"He's got a good arm and a good idea of what he wants to do," Uggla said.
The Astros' bullpen was equally impressive.
The RBI single by Uggla was the Braves' last hit of the game, as three relievers combined to retire all but one batter.
Wilton Lopez hit Uggla with one out in the ninth inning, but then got pinch-hitter Juan Francisco to ground into a game-ending double play as he recorded his first save of the season.
For the Braves, it was a night of missed opportunities.
"Overall, I thought Maholm pitched very well," Gonzalez said. "We just didn't hit."