Cunningham, in his first start with San Diego, drove a changeup away over the fence in center field off Toronto starting pitcher Brett Cecil (7-3) for a four-run lead. Cunningham later added a ground-rule double and a walk.
"I don't even know if it would have been a strike," said Cunningham, who became the first player in franchise history to have his first hit with the club be a grand slam.
"It was real nice. There were times when I was negative with Oakland. But here, sitting and watching, you're going to learn a lot."
Starting and swinging isn't bad, either, though Cunningham hadn't done much of either since being recalled from Triple-A Portland on June 11 when Matt Stairs landed on the disabled list with a strained right knee.
In fact, Cunningham -- who appeared in a combined 45 games with the A's from 2008-09 -- had two at-bats in his first four games with the Padres. Cunningham previously had two home runs with the A's.
"It's 400-plus feet out where he hit it. I don't know how it got out," Cecil said of the 404-foot home run. "He must have some strong wrists, because he was out in front of it. It could've been a better pitch, but I think it was still a good pitch."
Cunningham's big blast, coupled with 6 2/3 solid innings by starter Mat Latos (7-4) was enough to get the Padres (38-27) back to 11 games over the .500-mark and retain a half-game lead over the Dodgers in the National League West.
The Blue Jays, having lost seven of nine, fell to 35-31 heading into Wednesday's series finale.
Cunningham, while certainly not a household name, didn't exactly just fall off the turnip truck.
In fact, when the Padres made the deal with Oakland in January that sent third baseman Kevin Kouzmanoff and Minor League infielder Eric Sogard to the A's for outfielder Scott Hairston and Cunningham, San Diego general manager Jed Hoyer insisted that the 24-year-old wasn't a throw-in in the deal, and that he had impressive talent that could one day make him a fixture in the PETCO Park outfield.
Is that time now? It's tough to say, though the right-handed hitting Cunningham figures to perhaps start at least once over the next two games when the Padres face off against two left-handed pitchers -- Toronto's Ricky Romero on Wednesday and Brian Matusz of the Orioles on Friday.
"I like those, whoever hits them," said Padres manager Bud Black. "But it's great to see a young guy come up, make the start and contribute in such a big way. That was great for Aaron."
Latos lowered his ERA to 3.19 in 13 starts after retiring the first 11 batters he saw. He allowed two runs on four hits with one walk and seven strikeouts. Latos was able to mix his mid-90s fastball with his slider and changeup to keep the Blue Jays off-balance.
Staked to a 5-0 lead after three innings, Latos allowed two runs in the fourth inning after consecutive RBI singles by Alex Gonzalez and Lyle Overbay, but he fanned John Buck to end the inning.
Latos retired the next six hitters he faced before Gonzalez reached on a single to start the seventh inning.
"I think I started to nit-pick a little bit, just started to nibble on the corners instead of just going after them," Latos said. "This is a good-hitting ballclub to begin with, so if you make a mistake, and they start to adjust, they started to get some base hits there.
"After I finally got that third out, me and [catcher Nick Hundley] kind of talked about it, and I just told him, 'Hey, I feel like they were kind of leaning over the plate a little bit, looking for the off-speed,' and we weren't going in as much. We kind of changed it up and decided we were going to go inside a little bit."
Toronto manager Cito Gaston was impressed with the fastball Latos showed on Tuesday, as well as what relievers Joe Thatcher, Mike Adams and Ryan Webb offered.
"He's got good velocity, but all those guys do," Gaston said. "It seems like everybody that comes out of the 'pen throws 95, too. They've got some pretty good arms over there and he's one of them. He's a good-looking young kid."
The Padres added three runs in the eighth inning and were able to give closer Heath Bell and Luke Gregerson, two of their primary three late-inning relievers, the night off. Bell, in fact, has pitched only once since June 7, a span of eight games.