Reliever Aaron Loup (3-2) replaced Edgar Garcia with one on and one out. After Cavan Biggio reached on catcher's interference, Grichuk gave Toronto a 5-3 lead with his seventh home run.
Grichuk soon had to exit his spot in center field.
''He deserves all the credit for starting the game and trying to play, and then we had to take him out because it got really tight after that,'' Toronto manager Charlie Montoyo said. ''He started the game with his back hurting a little bit but he said, `I want to play it's a big game.'''
Lourdes Gurriel Jr. also homered for the Blue Jays, and Thomas Hatch (2-1) worked two scoreless innings for the win. He got his first big league victory in Friday's game against the Rays.
Jordan Romano worked the ninth for his second save. The right-hander got his first career save preserving Hatch's win on Friday.
Toronto is 14-13 and third in the AL East.
''Honestly I feel like today was the biggest win of the year,'' Montoyo said. ''I might be saying that for every game the rest of the year. But against that team ... to go 2-2 ... that's why I felt like today was the biggest win of the year.''
Yoshi Tsutsugo and Willy Adames homered for Tampa Bay. Oft-injured Rays center fielder Kevin Kiermaier was hit on the right foot by a pitch in the sixth and left after the seventh.
X-rays were negative but Kiermaier is not expected to start Tuesday night against Baltimore.
The Rays reached the midway point of the regular season at 19-11 after winning 11 of 14 and are in a tight race with the New York Yankees in the AL East.
Tampa Bay is missing eight pitchers due to injuries, including ace Charlie Morton.
''Look, we've got to be pretty pleased with where we're at 30 games given the injuries,'' Rays manager Kevin Cash said.
Ji-Man Choi opened the Rays eighth with a single off Rafael Dolis and went to second when Tsutsugo walked. Choi scored to make it 5-4 on shortstop Santiago Espinal's throwing error while attempting to complete a double play on a grounder by Joey Wendle.
Dolis avoided further damage by getting a double play grounder from Adames.
Toronto got the run back on Biggio's RBI double in the ninth.
The Rays went up 3-1 on Adames' opposite-field, two-run homer down the line in right off Tanner Roark in the fourth.
Adames also had an outstanding play at short in the sixth, sliding into the outfield to field a grounder and throw out Travis Shaw at first.
Gurriel ended Rays starter Blake Snell's day with a solo homer with two outs in the sixth that got the Blue Jays within 3-2.
Snell allowed two runs, four hits and struck out nine.
''It's definitely a tough loss,'' Snell said. ''It's a game we need to win.''
Tsutsugo, hitless in his previous 14 at-bats, put the Rays up 1-0 with a homer in the second. Toronto tied it at 1 when Vladimir Guerrero Jr. had an RBI double in the third.
Blue Jays: RHP Matt Shoemaker, placed on the 10-day IL Sunday, has a lat strain and his status is week to week. ... RHP Trent Thornton, who left his start Sunday after one inning with right elbow inflammation, was placed on the 10-day IL.
Rays: Morton (right shoulder inflammation) will throw a 25-pitch bullpen session Tuesday.
Blue Jays: RHP Chase Anderson (0-0) will go against Boston LHP Kyle Hart (0-1) on Tuesday night in Buffalo.
Rays: RHP Tyler Glasnow (0-1) and Baltimore LHP Tommy Milone (1-3) are Tuesday night's starters in Tampa Bay.
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