Calhoun and Laureano each had three hits in the rubber match of the three-game series. Their decisive hits in the 11th came against Jay Jackson (3-1).
Emmanuel Clase (2-7) pitched 1 2/3 innings for Cleveland, allowing one run in the 11th. Jose Ramirez added a two-run homer for Cleveland.
Vladimir Guerrero Jr. and Davis Schneider each hit a two-run home run for the Blue Jays. George Springer added a solo shot.
Toronto left-hander Yusei Kikuchi allowed four runs, six hits and two walks with eight strikeouts in six innings.
Cleveland right-hander Noah Syndergaard allowed five runs, four hits and three walks while striking out three in six innings.
Toronto took a 2-0 lead in the first. Brandon Belt walked and Guerrero hit his 20th homer of the season, a blast to left.
Cleveland tied the game in the third. Myles Straw walked with one out, Steven Kwan's grounder forced Straw at second and Ramirez hit his 21st homer of the season.
Cleveland took a 4-2 lead in the fourth. Calhoun led off with a double, took third on Laureano's single and scored on Tyler Freeman's single. Straw added a two-out RBI single.
Springer led off the home fourth with his 17th homer of the season and then made a spectacular catch in right center on a sinking drive by Ramirez in the fifth.
Santiago Espinal replaced Bo Bichette (right quadriceps tightness) at shortstop for the Blue Jays in the top of the sixth. Toronto third baseman Matt Chapman (inflamed finger) also left the game in the sixth inning.
Springer had an infield single with one out in the Toronto sixth and Schneider followed with his fifth homer in 11 career major league games, putting the Blue Jays in front 5-4.
Cleveland took a 6-5 lead in the eighth. Toronto reliever Tim Mayza walked Calhoun, who took third on Laureano's double. Andres Gimenez followed with a two-run double over the bag at first.
In the bottom of the frame, Trevor Stephan retired Springer on a fly to the wall in center before Schneider doubled and scored on Daulton Varsho's bad-hop single past first.
—Field Level Media