As a matter of fact, the Toronto Blue Jays had been winning a lot as well.
With right fielder Jerry Sands hitting a single through the left side of the infield in a two-run seventh for the go-ahead run, the Indians (64-66) extended their win streak to six games with a 4-2 victory over the Blue Jays.
"He's one of the best in baseball," Blue Jays manager John Gibbons said of Salazar. "That's no secret. Cleveland's pitching top to bottom is as good as anybody's in baseball. He's got a good, quick arm, plus he got the ball down more than we've seen in the past. We haven't seen him a lot."
The Blue Jays (74-57) finished August with a 21-6 record, the best winning percentage for one month in franchise history.
"We've won a lot of baseball games and that's good," said Price who came to Toronto in a trade with the Detroit Tigers. "I don't know what our record was this month but we've won a lot more games than we've lost. If we continue to play baseball the way we have since I've been here, good things will happen."
Price (13-5) allowed six hits, one walk and three runs in seven innings to take his first loss against four wins in six starts with the Blue Jays.
Salazar (12-7) held the Blue Jays to six hits, one walk and two runs.
"He didn't take any hitters off, because you can't," Indians manager Terry Francona said, referring to the hot Blue Jays lineup.
Salazar was battling illness that forced him to miss his scheduled start Friday.
"We were keeping an eye on his endurance because of that," Francona said. "I'm glad we waited a few days or that would have been more of an issue."
"I got tired quick," Salazar said. "In the fourth inning, I was dead tired. I had to hold on and try to come back. I lost six pounds in two days and I wasn't able to work out like I normally do in between outings.
"I was off my routine for about six days. It's tough to come back and try to keep good energy the whole game. I just tried to put in my mind 'You need to attack, you need to keep attacking. You can't give up right now.' In your mind, you know you want to be aggressive but your body is dead. I just want to go home and sleep right now.
Bryan Shaw replaced Salazar for the eighth inning.
The right-hander allowed a two-out single to right fielder Jose Bautista and that brought designated hitter Edwin Encarnacion, who extended his major-league-best hit streak to 26 games with a sixth-inning single, to the plate.
The Indians went to right-hander Cody Allen, their closer. Encarnacion doubled to left to send Bautista to third. Shortstop Troy Tulowitzki was walked intentionally. Justin Smoak, who entered the game as a defensive replacement at first base in the seventh, struck out to leave the bases loaded.
Allen stayed in the game for the ninth and earned his 28th save despite allowing one-out singles to center fielder Kevin Pillar and second baseman Ryan Goins. After left fielder Ben Revere fouled out to third, third baseman Josh Donaldson, who had a two-run triple in the fifth, struck out to end the game.
The Indians had taken the lead in the seventh. First baseman Carlos Santana walked with one out and designated hitter Ryan Raburn doubled to right-center to tie the game and took third on the throw home. Sands gave Cleveland a 3-2 lead with a two-out single to left.
The Indians added a run in the ninth against right-hander LaTroy Hawkins on singles by catcher Yan Gomes and pinch-hitter Lonnie Chisenhall. Donaldson was charged with an error on his throw to third that allowed Gomes to score.
The Indians scored in the first inning after second baseman Jason Kipnis led off with his 37th double of the season.
Goins unsuccessfully tried for the out at third after fielding a grounder from Indians shortstop Francisco Lindor. Kipnis scored when left fielder Michael Brantley bounced to Goins to start a double play.
Goins extended his hitting streak to a career-best 10 games when he singled with two outs in the fifth. Revere followed with his second infield hit of the game and Donaldson scored both with his first triple of the season to put Toronto up 2-1.
NOTES: Mark Shapiro is stepping down as Indians president to become the Blue Jays' president, effective at the end of the season, both teams announced Monday. Current Blue Jays president Paul Beeston is retiring at the end of the season. ... Blue Jays LF Ben Revere was in the leadoff spot and SS Troy Tulowitzki, who had been batting first, hit fifth for the second game in a row on Monday. ... The Blue Jays are expected to call up four or five players when rosters expand Tuesday. ... The Indians will activate INF Chris Johnson (left index finger infection) and RHP Gavin Floyd (right elbow fracture) from the disabled list Tuesday. ... RHP Shawn Armstrong will join the Indians from Triple-A Columbus on Tuesday. ... RHP Cody Anderson (2-3, 4.30 ERA) will start for Cleveland on Tuesday against Toronto RHP Marco Estrada (11-8, 3.19).