Cardinals catcher Tres Barrera was responsible for the only hit and run Senga allowed, a solo shot to left in the second.
Francisco Lindor and Pete Alonso hit solo home runs and Tim Locastro hit a pair of RBI doubles and scored on a throwing error for New York.
The Rays got their two runs from solo homers by Jose Siri and Randy Arozarena.
Jake Rogers hit his third home run of spring training for the Tigers.
The Athletics, who have flirted with a move to Las Vegas, played a two-game spring training series this weekend at Las Vegas Ballpark.