Happ fell to the ground clutching his head after being hit by a firmly hit line drive from Desmond Jennings in the second inning and was subsequently taken to Bayfront Medical Center for tests.
"From what it sounds like so far, he's in stable condition, he's conscious and that's all we know so far," Blue Jays right fielder Jose Bautista told mlb.com.
"We're hoping he recovers well and it doesn't get serious. There's always a chance of concussion when you hit your head like that, and we're hoping he doesn't get any symptoms like that."
The second turned into a four-run inning for the Rays, and they led 4-1 heading into the seventh, but the Blue Jays battled back with five runs in the last three innings, including a two-run homer from Colby Rasmus and a go-ahead ninth-inning solo shot from Maicer Izturis.
Matt Harvey allowed just one hit in nine scoreless innings, striking out a career-high 12, before the New York Mets beat the Chicago White Sox 1-0 in the 10th.
Harvey's performance, allowing just one base-runner all night, was not enough for his fifth win of the season as the Mets could not get on the board until pinch hitter Mike Baxter drove in a walk-off run in extras.
Alex Rios spoiled Harvey's bid for a perfect game with an infield single in the seventh.
Scott Diamond hurled seven scoreless innings to lift the Minnesota Twins to a 6-1 win over the Boston Red Sox.
Diamond allowed three hits, striking out two and walking none, while Ryan Doumit led the offence with his first home run of the season.
Boston's only run came in the ninth on a solo shot from Jarrod Saltalamacchia, batting because of a collision in the field between David Ross and Will Middlebrooks which saw both players exit the game.
Nate Schierholtz clubbed a two-run homer as the Chicago Cubs beat the St Louis Cardinals 2-1 to end their rivals' six-game winnings streak.
Travis Wood struck out eight in 6 2/3 innings, allowing one run on an Allen Craig long ball.
Jorge De La Rosa threw six shut-out frames to help the Colorado Rockies to a 2-0 victory over the New York Yankees.
Carlos Gonzales provided all the offence the Rockies needed with a two-run shot in the sixth.
Garrett Jones hit a two-run jack and Andrew McCutchen had four hits as the Pittsburgh Pirates beat the Seattle Mariners 4-1.
Zach McAllister pitched 7 2/3 scoreless innings and the Cleveland Indians beat the Oakland Athletics 1-0.
Will Venable homered and drove in three to lift the San Diego Padres to a 5-1 win over the Miami Marlins.
Yuniesky Betancourt and Aramis Ramirez went yard in the Milwaukee Brewers' 6-3 win over the Texas Rangers, while the Cincinnati Reds beat the Atlanta Braves 5-4.
The Houston Astros overcame the Los Angeles Angels 7-6, the Baltimore Orioles were 4-3 winners over the Kansas City Royals, the Philadelphia Phillies beat the San Francisco Giants 6-2 and the Arizona Diamondbacks saw off the Los Angeles Dodgers 5-3.
The game between Washington and Detroit was rained off.