With two outs and a man on first in the ninth, Evan Longoria hit a sharp grounder that went off the glove of a diving Aaron Hill in the hole between first and second base to spoil the no-hit bid. It left men at the corners, but Morrow struck out Dan Johnson with a high fastball to end the game.
Morrow (9-6) struck out a career-high 17 batters, which is the most by a pitcher this season, and also walked two while throwing 137 pitches, 97 for strikes.
Vernon Wells drove in the lone run for the Blue Jays, who have won five of their last six. Wells left after the sixth inning with a dislocated toe on his right foot that he suffered while making a leaping catch at the wall on a Ben Zobrist fly ball.
Andy Sonnanstine (2-1) was the tough-luck loser after giving up just one run and three hits with three walks and a strikeout over 5 1/3 innings for the Rays, who have dropped five straight.
This game was a far cry from Saturday's 17-11 contest, which saw nine home runs, eight by Toronto.
Toronto got on board in the first as Yunel Escobar drew a one-out walk, went to second on Jose Bautista's groundout and came home on a single from Wells for a 1-0 lead.
Morrow dominated Tampa Bay through the first six innings, allowing just a leadoff walk to Johnson in the second while striking out 11, including the all three batters in the first.
He struck out the first two batters of the seventh, but Johnson reached base when Lyle Overbay misplayed a grounder. Morrow then struck out Matt Joyce to end the frame.
In the eighth, Morrow struck out John Jaso to start the frame, blew a fastball past B.J. Upton for his 16th strikeout and got Reid Brignac to fly out to center.
Morrow has won his last four starts. He is 7-1 at home this season and 2-1 against Tampa Bay in his career...Sonnanstine got the start in place of Jeff Niemann, who was scratched with a sore right shoulder...Toronto hosts Boston for three games starting Tuesday...Tampa Bay continues its road trip in Detroit on Monday...Each team has won six times in the series this season.