Cardinals catcher Yadier Molina hit a solo home run in the top of the seventh inning off Cueto to give St. Louis an Opening Day 1-0 win over Cincinnati.
Wainwright reached career win number 100 Monday striking out nine batters and allowing three hits and four walks in seven shutout innings.
Cueto matched the Cardinal pitcher step for step giving up just three hits and striking out eight over seven innings, but Molina's 372-foot blast to left was the difference.
Molina finished the game 2-4 at the plate with the first homer of the season for the club. Matt Adams was the only other Cardinal with a multi-hit game.
The Reds and Cards are off Tuesday. Their series will continue Wednesday in Cincinnati with Michael Wacha getting the start for St. Louis.