Japanese Fukudome, who batted .257 last season, hit a three-run homer in the eighth to complete the scoring and lift his average for this campaign to .371.
Micah Hoffpauir, subbing for the injured Derrek Lee, belted a homer and Rich Harden held the in-form Cards to two runs in six innings at Busch stadium to help the Cubs end a four-game losing streak.
"I think it is important to let manager Lou (Piniella) know I'm comfortable against left-handed pitchers," a smiling Fukudome told reporters through an interpreter.
Harden (2-1) struck out nine and served up four hits, including solo homers by Yadier Molina and Rick Ankiel, for the win.
"This was definitely an important game because we'd lost a few in a row," Harden said. "You want to treat every start the same but you also want to stop a slide like that.
"I wasn't feeling too great early on and I wanted to pick up the intensity a little bit, give everything I've got. Then it worked a little better."
Lee hit an RBI double in Chicago's three-run first inning before leaving the game before the start of the bottom half because of neck spasms.
"It locked up on me again," the 33-year-old right-hander said. "I think I slept funny and I woke up stiff.
"I had a good at-bat and then have to come out. Sometimes things aren't rolling your way. What can you do?"
St Louis, who rode Albert Pujols's second grand slam of the season to pummel Chicago 8-2 on Saturday, had been seeking a 10th consecutive home win to wrap up a three-game series sweep.
However, the Cardinals trailed throughout after Todd Wellemeyer gave up six runs in five innings, including three in the top of the first.
"It didn't go too well," Wellemeyer said. "I might have been a little too pumped up there in the first inning. When you get some bloop hits, you start thinking a little bit too much.
"You start pressing a little too much. By the time the third inning came around, I quieted myself down and became much more efficient."
