Making his third start of the season, Mills (1-2) allowed six runs and five hits in three innings. The left-hander walked two and struck out five.
All six runs against Mills came in the third, when Oakland batted around and collected three extra-bases hits on pitches up in the zone.
"He just didn't have the ability to work ahead in the count and finish the hitter off when he was ahead in the count," Toronto manager John Farrell said. "It was more about location than anything."
Mills said his confidence won't be shaken by the poor performance.
"It's not the first time I've had a bad inning and it won't be the last," he said. "It's not the end of the world, but I feel bad that I wasn't able to help the team get off to a good start."
Swept in a three-game series at last-place Seattle to open their cross-continental journey, Oakland recovered by taking two of three in Tampa Bay and two of three from the Blue Jays.
"We came into two places that are tough to play against two good teams that swing the bat," Oakland manager Bob Melvin said. "To take two out of three in both these places with what we had been doing on the road is a nice pick-me-up and a nice confidence rebuild after a tough series in Seattle."
The Athletics are 22-40 on the road this season, and have won just 11 of their past 42 away from home.
Oakland failed to hit a home run for the first time in nine games but still finished with its most runs since scoring 13 against Tampa Bay on July 27. Oakland's season-high is 14 runs, set May 17 against the Angels.
Matsui had a 15-game hitting streak snapped Tuesday and was hitless in 10 at-bats before an RBI single in the third. He grounded out in the fourth but singled again in the sixth, seventh and ninth to finish 4 for 6. Matsui, who was hitting .209 at the All-Star break, has raised his average to .268.
"The run that he's on is remarkable," Melvin said. "I don't know that I've been around a run like that, a consistent run. He never ceases to amaze you."
It was something of an adventurous day on the bases for Matsui, who was hit on the lower left leg by a pitch Wednesday and played despite minor swelling. Trotting home from second on Jackson's triple in the third, he was nearly caught by Josh Willingham, who crossed the plate just a few feet behind.
"I didn't know if Hideki was going to pass the baton to him," Melvin joked.
Willingham, who said he was gaining on Matsui despite "jogging," made sure his teammate knew he was closing fast.
"He was right behind me yelling at me 'Run, Matsui, run!'" Matsui said through a translator.
The Japanese slugger was nearly thrown out at second after lining an RBI single to right in the sixth, but shortstop Yunel Escobar didn't see him coming and fired the relay to the plate, allowing Matsui to take second.
"I was trying to trick them," he joked. "Apparently I was just making a fool out of myself. I actually even laughed at myself afterward."
Guillermo Moscoso (5-6) allowed two runs, one earned, in six innings to earn the win. He walked two and struck out six.
"I felt pretty good, I was making my pitches," Moscoso said. "I was working the slider today. That was the key, to get ahead in the count with the first two pitches and I was able to do whatever I wanted."
J.P. Arencibia hit his 19th home run for Toronto, a solo drive to center in the seventh, but it wasn't enough for the Blue Jays.
Cliff Pennington started Oakland's six-run third with a two-run double. Matsui followed with an RBI single and, after Willingham was hit by a pitch, Jackson tripled and scored on a wild pitch.
Moscoso was perfect through the first three innings before walking Escobar to begin the fourth. One out later, Jose Bautista walked to put runners at first and second for Adam Lind, who grounded to shortstop. Trying for the double play, Pennington's relay to second base sailed into right field for an error, allowing Escobar to score and sending Bautista to third. Bautista came home one batter later on Edwin Encarnacion's infield single.
NOTES: Athletics OF Coco Crisp (right calf) missed his fourth straight game and is expected to sit out the upcoming three-game series against Texas. ... Encarnacion has started taking fly balls in left field, Farrell said, and could see some time in the outfield before the end of the season. ... Brandon Morrow and the Blue Jays host Ervin Santana and the Los Angeles Angels on Friday night.