Jimenez (7-4) dodged constant trouble in six innings, allowing five hits with two walks and four strikeouts.
Cody Allen, Joe Smith and Chris Perez blanked Toronto over the final three innings. Perez allowed two hits in the ninth, but earned his 10th save as the Indians recorded their American League-leading 11th shutout.
The Indians managed only four hits. Nick Swisher and Michael Brantley had RBI singles in the fourth when the Indians put together a walk and three straight singles off starter Josh Johnson (1-4), who gave up two runs in seven innings.
Asdrubal Cabrera added a sacrifice fly in the eighth.
Toronto stranded nine runners, with seven in the first five innings, and was 1 for 12 with runners in scoring position. Maicer Izturis and Rajai Davis singled with one out in the ninth, but J.P. Arencibia struck out and pinch hitter Josh Thole lined out to shortstop.
The Blue Jays' best threat against Jimenez came in the fourth when they had runners on first and third with nobody out. Colby Rasmus started the inning with a double and took third on Izturis' single. Davis hit into a fielder's choice and stole second but Arencibia struck out and Emilio Bonifacio flied out to deep right.
Jimenez's strongest inning came in the sixth, the only time he retired the side in order.
Johnson retired the first 10 hitters before Cabrera drew a one-out walk in the fourth. Johnson fell behind 3-0 before a foul ball and called strike ran the count full. Cabrera walked on an inside pitch before Jason Kipnis hit a hard ground ball past shortstop Jose Reyes for Cleveland's first hit.
Swisher bounced a single through the right side that scored Cabrera and moved Kipnis to third. Brantley's line single to right made it 2-0.
Johnson beat Baltimore on June 23 for his only win of the season, allowing four runs in six innings. He was sidelined from April 21 to June 9 with right triceps inflammation. Johnson won his first career start against the Indians on May 20, 2012, while pitching for Miami. Toronto has lost each of Johnson's last three starts.
The Indians had lost five of six after winning five in a row. Cleveland lost three of four to Detroit, which leads the AL Central, including a 4-2 loss Monday in 10 innings. The Indians are 28-12 against teams below .500.
The Blue Jays are 5-10 since winning 11 straight from June 11-23.
Cabrera was 0 for 2 and is hitless in his last 21 at-bats.
NOTES: The start of Tuesday's game was delayed by rain for 36 minutes. ... RHP Danny Salazar will be recalled from Triple-A Columbus to start Thursday's game and make his major league debut for the Indians. ... Blue Jays OF Melky Cabrera (left knee) is scheduled to begin a minor league rehabilitation assignment Friday, but will not be activated until after the All-Star break. He was placed on the 15-day disabled list on June 28. ... Blue Jays 3B Brett Lawrie (left ankle) had his rehab assignment shifted to Triple-A Buffalo after playing seven games at Single-A and Double-A. ... The Blue Jays have released C Ramon Hernandez from his contract with Buffalo. ... Indians RHP Justin Masterson (10-7, 3.78 ERA) takes on Blue Jays RHP Esmil Rogers (3-4, 3.84) in the second game of a three-game series Wednesday. Cleveland traded Rogers to Toronto for INF Mike Aviles and C Yan Gomes in November.