Closer Roberto Osuna, who did not pitch on Friday because of anxiety issues, worked the ninth. He gave up a single and struck out three in one scoreless inning, although it was not a save situation.
"It's slowly getting better, but I'm getting better, so that's a good thing for me," Osuna said.
With Osuna unavailable Friday, the Toronto bullpen yielded a four-run ninth. None of the Blue Jays' three relievers allowed a run Sunday.
Liriano (4-3) picked up first victory since June 2 and only his second since April 29. Liriano is 100-95 since breaking into the majors in 2005 with Minnesota.
"It means a lot to me," Liriano said of reaching 100. "I feel like I had to battle through a lot and go through a lot of stuff and being injured a lot, but things happen for a reason. I'm just thankful and very happy."
He stymied the Royals on six hits and two runs. He was pulled in the seventh after Salvador Perez started the inning with a double and Cheslor Cuthbert walked.
Danny Barnes replaced Liriano and retired the next three Royals on fly balls to end the threat.
Bautista is hitting .381 with four walks in five games since moving to the top of the Blue Jays' order.
"Generally he's always a high-on-base guy," Blue Jays manager John Gibbons said. "He gets on base and draws a lot of walks, and he's dangerous when he's hitting. He had a nice, big day today, which we needed. You know what, he strikes fear into pitchers. A lot of times what happens in baseball, even the good starters, that first inning can be a little rocky."
The Blue Jays snapped a 2-2 tie with a five-run sixth inning on two hits, three walks and a Cuthbert error. Josh Donaldson's double off Peter Moylan plated Bautista and Steve Pierce. Moylan had walked Bautista with the based loaded for the first run of the inning.
Rookie left-hander Scott Alexander (0-2) started the inning by giving up a pinch-single to Darwin Barney and walking the next two batters before Moylan replaced him.
Bautista homered with Ryan Goins aboard in the fifth to tie the score at 2. Bautista got the green light on a 3-0 Jason Hammel pitch and hammered it an estimated 450 feet to the left-field grass.
Hammel was pulled after five innings, allowing two runs, five hits and three walks while striking out six. He threw 105 pitches.
"A very small strike zone today contributed to him getting his pitch count up," Royals manager Ned Yost said.
The Royals were unanimous in their belief that plate umpire John Tumpane had a strike zone not much larger than a postage stamp.
"It was definitely small," Hammel said. "For what we did in the bottom of the zone execution-wise, I think we should have been rewarded a little bit more. It's tough when in big situations when you make a pitch and it's not called a strike, it can change the outcome big time."
Moylan thought he threw a strike to Bautista before walking him with the bases full. He had words for Tumpane. After he was pulled, Moylan had additional words for the umpire and was ejected.
"I don't usually get emotional out there, but I just sort of had enough," Moylan said. "I don't want to say there's no accountability, but I go out there and I'm trying to get Scotty out of a situation and I think I can do my job. That sort of call changes sort of my mindset. I've got to do a better job of locking back in and not walking him."
Hammel kept the Blue Jays off the board until the fifth inning but required 64 pitches to navigate through the first three innings. He gave up a double to Russell Martin in the first. He walked Troy Tulowitzki and yielded a single to Pillar in the second.
In a 24-pitch third inning, Donaldson walked and Justin Smoak singled with two outs.
The Blue Jays, who lost the first two games of this series, have not been swept in Kansas City since 1993.
NOTES: Royals LHP Danny Duffy, who went on the disabled list May 29 with a strained oblique, made his initial minor league rehab start Saturday night. He threw 48 pitches in 2 2/3 innings for Triple-A Omaha, giving up two runs and two hits, including a home run to the last batter he faced. ... The Blue Jays and Royals are both idle Monday. Toronto returns home Tuesday to play Baltimore. RHP Kevin Gausman and Orioles RHP Joe Biagini are the Tuesday probables at Rogers Centre. The Royals will start rookie LHP Matt Strahm on Tuesday at Detroit. The Tigers will counter with RHP Justin Verlander.