Toronto was coming off an 8-7 victory over the Rays on Monday night in which the Blue Jays rallied from a 7-0 deficit.
Adam Lind put the Blue Jays up 1-0 in the second on his first homer this season. Cody Rasmus cut the deficit to 4-3 on a two-run homer in the seventh.
"It took us a few innings to regroup," Lind said. "The energy in the dugout was very sad and we weren't really in the mood. I think that was obvious, and then we got some hits and got our minds off things that were bad and got our minds pointed in the right direction."
Steve Delabar (3-1) threw two scoreless innings before Casey Janssen pitched the ninth for his ninth save. The Blue Jays have won three in a row for the first time this season.
Tampa Bay starter Roberto Hernandez went six innings, allowing one run and five hits. He had seven strikeouts and one walk.
Maddon was ejected in the second for arguing by plate umpire Marty Foster prior to Happ getting hurt.
Foster ruled that Sean Rodriguez's hand missed the plate as he tried to score from third during a slide on Jose Molina's bunt. Maddon was tossed after swiping his hand across the plate where the manager thought Rodriguez had touched it.
Foster also threw out Edwin Encarnacion after the Toronto first baseman struck out to end the ninth.
NOTES: Rays RF Ben Zobrist rejoined the team after missing two games following the death of his grandmother. ... Toronto secured at least a split in the four-game set, which snapped Tampa Bay's streak of winning 17 straight home series against the Blue Jays. ... A group of injured Toronto pitcher rehabbing at the team's complex in nearby Dunedin were at the ballpark.