The Royals (75-77) took the final two games of the three-game set to win the season series with the Blue Jays (71-82) four games to two.
Vargas (17-10) held the Blue Jays to two hits and three walks while striking out seven. The left-hander has won three straight starts. He is tied with Boston's Chris Sale and Cleveland's Corey Kluber for the most wins in the American League.
Mike Minor pitched a perfect ninth to earn his second save of the season.
Toronto left-hander J.A. Happ (9-11) allowed seven hits, two walks and one run while striking out six in 6 2/3 innings. He had won his previous three starts.
The only run of the game was scored in the third inning. Alex Gordon walked with one out, took second on a two-out single by Lorenzo Cain and scored on Cabrera's single.
Happ induced two double-play grounders after the Royals had their first two hitters reach base in the fourth and sixth innings.
In between, he struck out the side in the fifth.
Happ was replaced by Dominic Leone with two outs in the seventh after a walk to Gordon put runners at first and second. Mike Moustakas had opened the inning with a single and was forced at second base by Alcides Escobar on a grounder to third.
Leone ended the inning on a grounder to short by Whit Merrifield that forced Escobar at second.
Peter Moylan replaced Vargas with one out and the bases empty in the seventh inning.
After Kevin Pillar grounded to third for the second out, Ryan Buchter was brought in to face pinch hitter Michael Saunders, who gave way to another pinch hitter, Rob Refsnyder, who lined out to second.
Kansas City's Joakim Soria pitched a perfect bottom of the eighth with two strikeouts.
NOTES: Blue Jays RF Jose Bautista whiffed in the sixth inning to set a club record with 160 strikeouts in a single season. OF Jose Canseco (1998) and INF Kelly Johnson (2012) each struck out 159 times in a season. ... Royals C Salvador Perez had two singles to extend his hitting streak to five games. ... Blue Jays RHP Marco Estrada (9-8, 4.84 ERA) will oppose New York Yankees RHP Masahiro Tanaka (12-11, 4.73) on Friday in the opener of a three-game series that will close out Toronto's home schedule. ... Royals RHP Jason Hammel (8-12, 5.05) will face White Sox RHP Reynaldo Lopez (2-3, 4.84) Friday to open a three-game series at Chicago.