Tigers starter Justin Verlander (0-1) carried a 2-0 lead into the ninth but couldn't hold it.
Evan Longoria followed with a game-tying single.
Reliever Daniel Schlereth issued a walk to pinch-hitter Elliot Johnson, then gave way to Jose Valverde, whose 3-2 delivery to Zobrist was grounded up the middle for the margin of victory.
The comeback made a winner of James Shields (1-0), who yielded two runs on six hits over eight innings, walking one and striking out five.
Fernando Rodney tossed a scoreless ninth for his third save as the Rays evened their three-game series with the Tigers.
Miguel Cabrera went 2-for-4 with an RBI single for Detroit, which endured its first loss of the season after opening with four straight victories.
UPI Sports Results for September 20, 2014
UPI Sports Results for September 19, 2014