Morales, whom the Blue Jays signed to a three-year, $33-million contract, gave Toronto a 2-1 win over the Baltimore Orioles with a walk-off home run in the ninth inning.
The Blue Jays breathed a huge sigh of relief because it ended a seven-game slide in the worst start in the franchise's 40-year history. The Jays raised their record to 2-9, last in the American League East.
The AL East-leading Orioles, who were riding a three-game winning streak, dropped to 7-3.
Toronto recorded the win in front of an announced paid crowd of 40,743.
"Hopefully this win will take us further," Morales said. "I try to do the same routine every day. I was getting a little bit unlucky, but you just got to trust yourself and keep doing what you've been doing since the beginning. I just stayed with it and it worked today."
Blue Jays' President Mark Shapiro felt particularly satisfied. He had made the decision to sign Morales when fan favorite Edwin Encarnacion opted for free agency and turned down a four-year, $20 million contract. He subsequently signed with the Cleveland Indians.
"Certainly coming on the heels of some frustration -- just because we've actually played pretty well but haven't hit -- it's an exhale moment more than anything," Shapiro said.
The teams finish their four-game series on Sunday at the Rogers Centre. Dylan Bundy (1-1) starts for Baltimore, with J.A. Happ (0-2) pitching for Toronto.
Blue Jays' relief pitcher Roberto Osuna (1-0) also had reason to exhale after getting the victory. He allowed the Orioles to tie the game 1-1 in the ninth when catcher Welington Castillo started things with a single. Outfielder Craig Gentry replaced Castillo, stole second and eventually made it home on two flyouts.
"Things aren't going the way we want to right now, but whenever it turns up in our way, it's going to be better," Osuna said. "I blew the save today, but they got my back. We came back, so that's a good win for us. Our confidence goes up. Hopefully we can tie the series tomorrow."
Tyler Wilson (1-1) was tagged with the loss.
Toronto received a strong pitching performance from Marco Estrada, who went seven scoreless innings and issued four hits, three walks, eight strikeouts, one wild pitch and one hit batter.
Estrada threw 109 pitches, 69 of them strikes. It was a significant improvement from his last start when he served up three home runs in a loss to the Tampa Bay Rays.
Baltimore's Alec Asher, appearing in his first game of the season after a recall from Triple-A Norfolk, had a good outing until he got into a jam in the seventh.
After hitting Jose Bautista, he was able to record the first out of the inning when Morales lined out to center field. Troy Tulowitzki followed up with a single up the middle to advance Bautista to second.
"I felt good," Asher said. "It's tough to get the loss. I feel like we battled as a team, but I felt good out there and hopefully continue that. I felt good (from) my last outing in Norfolk, and I just wanted to come up here and continue to throw the ball well and it worked out for the best."
Asher was charged with the run. In 6 1/3 innings, he issued three hits, one earned run, one walk, five strikeouts, one wild pitch and one hit batter. He threw 93 pitches, 59 of them strikes.
Hart, who replaced Asher, lasted 1 1/3 innings, and was charged with two hits and recorded two strikeouts.
"It what it is," Orioles' manager Buck Showalter said. "It's a long season. I think guys are mature enough to understand. (Asher) did his part and he's made a really good impression. I'll make a bet he gets another start again sometime this year."
NOTES: Toronto C Jarrod Saltalamacchia started for only the second time this season, giving Russell Martin a day off. Martin has been struggling this season with only two hits in 28 at-bats. ... Blue Jays 3B Chris Coghlan, recalled from Buffalo on Friday, was inserted into the lineup because manager John Gibbons thought he deserved a chance to play. ... Toronto CF Kevin Pillar started at leadoff in the batting order because 2B Devon Travis was given the game off. Pillar hit a single in his first at-bat. ... With the recall of Asher from Triple-A Norfolk, the Orioles optioned RHP Stefan Crichton to the Tides. ... Orioles SS Ryan Flaherty took the spot of J.J. Hardy in the lineup because manager Buck Showalter didn't want to play Hardy in all four games of the series because of the Rogers Centre's artificial turf.