The Pacific Coast League All-Star took a no-hitter into the eighth inning and combined with Winston Abreu on a one-hitter as the 51s blanked the Padres, 5-0.
Mills ended up striking out six and walking a pair over eight one-hit frames.
A fourth-round pick in the 2007 Draft out of the University of Arizona, Mills is in his third season with the Blue Jays' Triple-A affiliate. He went 1-0 with a 5.64 ERA in seven appearances, including three starts, for Toronto last year.
Mills was the PCL's starter and loser Wednesday in the Triple-A All-Star Game.
"It was a little different, coming off the All-Star Game and playing in a Midwest League park," Mills said. "I tried to treat the All-Star Game as bullpen work in my regular schedule."
Las Vegas and Tucson were concluding an unusual four-game set at Fort Wayne's Parkview Field, normally the home of the Padres' Class A Midwest League affiliate, the TinCaps. San Diego's Triple-A team played in Portland, Ore., last season, but its location for the 2011 campaign was uncertain until late last year. It was thought the Triple-A Padres might play nomadically, with a few games in San Diego and a few at the home of the California League's Lake Elsinore Storm. While the team found a home in Arizona, the TinCaps' invitation to visit was still accepted.
The 51s didn't seem to mind the unusual venue, taking three of the four games.
"It was pretty neat playing back here," Mills said. "I really enjoyed playing in the Midwest League [for Lansing in 2008] -- it was one of my best experiences as a pro.
"And as a pitcher, the park here is a little more friendly than some of the ballparks in the Pacific Coast League."
Las Vegas got off to a strong start Sunday as Darin Mastroianni opened the game with a double to center and scored on a two-out double by Adam Loewen.
Mills (8-7) took over from there.
The 26-year-old left-hander issued a two-out walk in the first to James Darnell, then set down the next 19 batters before Matt Clark broke up the no-hit bid with a leadoff single in the eighth. After a popup and a walk, Mills got out of trouble with a strikeout and a groundout.
"My command was solid today, especially after the first few innings," he said. "[Clark's hit] was on a 3-2 changeup. I struck him out on a changeup earlier in the game and I think I doubled it up in that at-bat. I might have left it up a little bit, but I'd throw that pitch again every time. He just hit it."
Mills exited after throwing 106 pitches -- 69 for strikes -- and matching the longest outing of his career.
Abreu struck out two in a perfect ninth to close out the 51s' sixth shutout of the season.
Jayson Nix provided a cushion for Mills with a three-run blast in the third, his third longball in four games since joining Las Vegas. The 51s' other four hits were doubles belonging to Mastroianni, Loewen, Ricardo Nanita and Manny Mayorson.
Tucson starter Jon Leicester (4-4) allowed five runs -- four earned -- on four hits and five walks over six innings. He struck out three.
The clubs return to more familiar surroundings Monday, with the 51s heading to Colorado Springs for a five-game series and the Padres returning to Tucson to host Tacoma.