Cabrera's tying, two-run single in the eighth completed the Reds' rally from a 6-2 deficit.
Ben Zobrist had two hits for Tampa Bay. He hit a leadoff single in the ninth and later scored on Hinske's single.
Evan Longoria had an RBI double for the Rays.
Starters Homer Bailey of Cincinnati and Edwin Jackson of the Rays each pitched two innings. Jackson is trying to earn a spot in the rotation.
"He was very composed out there," Tampa Bay manager Joe Maddon said. "We saw that from him last year even when he struggled."
Reds reliever Edinson Volquez gave up three runs in 1 2/3 innings. The Rays scored three runs after he hit Jonny Gomes with a pitch with two outs.
"He lost his concentration. Things began to unravel. He was one strike away from having a very good outing," Cincinnati manager Dusty Baker said.