Bourn also scored twice for the Astros who won for the 12th time in 16 games.
Astros starter Nelson Figueroa (5-2) pitched five innings to earn the victory. He allowed three runs on six hits. He struck out five and walked three. Figueroa was backed by four scoreless innings from the Houston bullpen, which allowed only one hit.
Cubs starter Carlos Silva (10-6), who made his first start since Aug. 1, was tagged for six runs on nine hits in five innings. In his previous start at Colorado, he left after recording only one out with an abnormal heart rate. Silva underwent a surgical procedure called cardiac ablation to correct the problem a week later. He returned after two rehab starts for Class A Peoria, but was far from regaining his stuff that helped him win his first eight decisions of the season.
Tyler Colvin drove in two runs on two hits for the Cubs.
Trailing 2-1 in the second inning, Wallace homered to tie the game. Tommy Manzella and Jason Castro followed with back-to-back singles. With two outs, Bourn hit a two-run double in the left-center gap to give the Astros a 4-2 lead.
Leading 4-3 in the fifth, Bourn led off with a single and stole before scoring on Jeff Keppinger's single. Hunter Pence followed with a double down the right-field line, scoring Keppinger from first without a throw.
Bourn led off the game with a triple to right-center and scored on Keppinger's RBI single.
In the first inning, Kosuke Fukudome led off with a double and score on Marlon Byrd's single. Byrd scored on Colvin's fielder's choice.
Micah Hoffpauir walked in the third inning and scored on Colvin's triple.
Cubs shortstop Starlin Castro spent his second game on the bench after not knowing how many outs there were in the seventh inning of Chicago's 18-5 loss to the Mets. The rookie came into the game with the third best batting average in the National League at .317.
NOTES: Before the game, a statue of Hall of Famer Billy Williams was dedicated by the Chicago Cubs outside Wrigley Field on Tuesday. The sculpture was unveiled before Chicago's home game against the Houston Astros. Williams was accompanied at the ceremony by his wife, Shirley. Also in attendance were former teammates Ernie Banks, Ferguson Jenkins, Ron Santo and Glenn Beckert, and Chicago dignitary Rev. Jesse Jackson.