The appearance marked Belisario's 2015 Major League debut and the 26th pitcher to be used by Tampa Bay this season, a new club record.
The veteran right-hander pitched the eighth and the ninth innings, allowing only a walk.
"Belisario, it was nice to see him get in there, pick up the last two innings for us," manager Kevin Cash said.
Belisario, who pitched with the Dodgers and White Sox before landing in Tampa Bay, was expected to be with the Rays on Opening Day, but fractured his non-throwing shoulder in Spring Training. After rest and rehab, he became a staple out of Triple-A Durham's bullpen, recording 17 saves. He opted out of his Minor League contract and was selected to the big league club Tuesday.
"We're just getting help from everybody, which is great," said Matt Andriese, the winning pitcher. "Throwing a shutout in general is good, but when five guys contribute, it's pretty solid."