With one out, Molina and Jay bounced back-to-back doubles just inside third base to make it 1-0.
Rookie Kolten Wong's deep fly ticked off Lake's glove for an error, putting Wong on second and Jay on third. Following an intentional walk to Daniel Descalso and fly out by Wainwright, Carpenter's hit up the middle drove in Jay and Wong.
The Cubs cut it to 3-1 in the sixth. David Dejesus, who had walked with two outs, scored on Lake's double to the gap.
Jay's three-run homer in the seventh off Russell, the second of four Chicago relievers, put the game away.
NOTES: Wainwright had a season-high 12 strikeouts on April 13 against Milwaukee. ... The 23-year-old Castro, one of the Cubs' most touted young players, has struggled much of this season. He entered Sunday hitting .244 with seven homers and 32 RBIs, and was 0 for 16 in his past five games. But Sveum was willing to give him another chance. "I don't think this kid can get better by not playing today and understanding the adversity that we all go through in a game," Sveum said before the same. ... Descalso, a left-handed batter, started at shortstop for St. Louis on Sunday against Jackson, a right-hander. He replaced right-handed hitting, Pete Kozma who played Saturday. Manager Mike Matheny stopped short of saying the two would platoon the rest of the season. "I am still comfortable with (Kozma's defense), but I think we've all been becoming more comfortable with the innings (Descalso) has been playing as well, and how he's swinging the bat at times. I think you're going to see both of them." Kozma, was hitting .223 entering the game and Descalso was at .254. ... Wong, one of the Cardinals' top prospects, started at second on Sunday and appeared in each game of the series after making his major league debut on Friday.