St. Louis was already ahead 6-1 following Jay's three-run homer off Russell in the top of the inning.
Wainwright allowed singles to Nate Schierholtz and Welington Castillo to open the bottom half, but the next batter, Donnie Murphy, was called out on a check swing.
Sveum disputed the call with plate umpire Phil Cuzzi from the dugout, then came onto the field to continue the argument following the ejection. Russell was tossed by third base umpire Tom Hallion.
"That's easily the worst checked-swing call I've ever seen. Sveum said. That's why the other umpires are there, to give him help."
Chicago starter Edwin Jackson (7-13) allowed three runs, but only one earned, through six innings. He walked four and struck out three.
Jackson has been stronger in the second half after an 1-8 start. He got little support on Sunday and his defense didn't help when Lake dropped a fly ball in center field for an error in the Cardinals' three-run second inning.
"In pitching, things are going to happen," Jackson said. "It was one of those things you try to battle down and do damage control.
"It definitely could have been a lot worse. You just try to keep them within striking distance."
St. Louis catcher Yadier Molina had two doubles in his third game back after two weeks on the disabled list.
Starlin Castro was back in the Cubs lineup a day after being pulled for making a mistake the day before, and had an infield single. Manager Dale Sveum said Castro had atoned for his mistake.
On Saturday, the shortstop dawdled after catching a popup in shallow left field, allowing a run to score and Sveum pulled Castro from the game.
Carpenter's single with two outs and the bases loaded drove in two runs as the Cardinals jumped ahead 3-0 in the second.