Lawrie sustained a broken right index finger when he was hit by a pitch in the second. The team didn't immediately announce how long the infielder would be out.
Bautista left because of tightness in his left leg. The All-Star outfielder had a single and a sacrifice bunt before leaving.
Cueto (7-5) gave up three runs -- one earned -- and leads the NL with a 1.86 ERA. He gave up seven hits and struck out eight while winning his third straight start.
Aroldis Chapman struck out the side in the ninth for his 13th save.
Cueto led off the fifth with a bunt single. One out later, Frazier lined his team-leading 17th homer of the season.
Edwin Encarnacion led off the Toronto eighth with his 24th home run, connecting against his former team.
The Reds used Encarnacion's error at first to take a 1-0 lead in the first. With Frazier on first and two outs, Brandon Phillips was safe when Encarnacion couldn't handle third baseman Juan Francisco's throw on a chopper. Jay Bruce converted the error with an RBI single.
The Blue Jays got help from two errors to take a 2-1 lead in the third. Munenori Kawasaki reached on first baseman Joey Votto's throwing error, Melky Cabrera singled and Toronto loaded the bases on Cueto's misplay of Jose Bautista's bunt. One out later, Colby Rasmus lined a two-run single.
Encarnacion, who a pair of three-run homers Friday night, homered off Cueto into the left-field seats.