Tyler Colvin and Marlon Byrd swatted solo home runs and Carlos Marmol picked up the save in a strong bullpen performance for the Cubs (1-2), who avoided being swept in their season-opening three-game series.
Martin Prado had three hits for the Braves (2-1) but the home side left seven runners in scoring position to fall to their first loss of the season.
Second-year starter Tommy Hanson allowed both runs during his 5 1/3 innings and struck out seven batters.
The Cubs had not begun 2010 on a positive note, having been destroyed 16-5 on Monday and edged by a late-inning home run 3-2 on Wednesday, but Chicago rebounded despite tallying just four hits.
Powered by home runs in the second and fourth innings, the Cubs pitched their way out of persistent trouble.
Wells faced a bases-loaded scenario in the third as well as a jam in the sixth where Atlanta had runners on first and third, but he induced double plays both times.
"You never want to put your back against the wall like that, but when you can calm your emotions and make some pitches and get out of it, it's pretty exciting," Wells said. "I never like to do that, but sometimes you can't help it."
Chicago used four relievers who combined to keep the game scoreless.
Touted Atlanta rookie Jason Heyward, who hit a home run in his Major League debut, was 0-for-4 with one strikeout.
(Reporting by Jahmal Corner in Los Angeles, edited by Patrick Johnston; To query or comment on this story email firstname.lastname@example.org)