"One of those games you love to be a part of," Murphy said.
Kluber pitched seven innings to win consecutive starts for the first time this season, and Carlos Santana and Yan Gomes homered as the Indians set season highs with 22 hits and 15 runs in winning for the sixth time in eight games.
"From top to bottom, we either took walks or got hits," Indians manager Terry Francona said." Just a good night all the way around."
Kluber (4-3) allowed two runs and four hits, walked one and struck out nine. The right-hander is 3-0 with a 2.04 ERA in his past five starts, with 47 strikeouts over 34 1/3 innings.
"I'm more and more impressed with him each time he goes out there," Murphy said. "He's got the stuff to be an ace."
Infielder Steve Tolleson came on to record the final out in the ninth inning after Gomes drilled a three-run homer off Neil Wagner. Throwing knuckleballs, Tolleson faced two batters, giving up a double to Chisenhall before Mike Aviles popped out.
It was the first time two Indians had five hits in a nine-inning game since Johnny Hodapp and Luke Sewell had five each against the Yankees on July 29, 1928.
The bottom four batters in Cleveland's lineup combined for 14 hits, 10 RBIs and five scored runs.
"That makes you feel good when you're getting contributions all up and down," Francona said. "That's the kind of team we have to be."
Michael Brantley, whose 11-game hitting streak ended in Tuesday's loss, doubled to open the fifth and scored when Santana followed with a homer into the second deck. Asdrubal Cabrera followed with a single, chasing Blue Jays starter Dustin McGowan.
McGowan (2-2) allowed four runs and nine hits in four-plus innings. He walked two and struck out three.
"All my pitches were fine tonight," McGowan said. "I just got hit hard."
McGowan is winless with an ERA of 9.19 in four home starts this season, but 2-0 with a 2.31 ERA in four road starts. He dropped to 0-3 with a 10.61 ERA in five career games against the Indians.
Cleveland capped it with a six-run, 10-batter ninth. Michael Bourn hit an RBI triple and scored on a base hit by Jose Ramirez. Murphy hit a two-run double and Gomes ended a 12-pitch at bat by homering.
Brantley left in the fifth with a sore back. He was replaced by Nyjer Morgan, who lasted just half an inning before spraining his right knee. Ramirez replaced Morgan, going in at second base as Aviles moved to left.
Francona said he wasn't sure whether Brantley or Morgan would be available Thursday. Morgan was wearing a brace to immobilize his leg after the game.
"We need to see how he shows up in the morning," Francona said of Morgan.
Tolleson is the seventh position player to pitch for the Blue Jays. ... This was the third five-hit game of Murphy's career. ... The last time Cleveland had two or more players with at least five hits in a game was July 10, 1932, when Johnny Burnett had nine and Earl Averill and Eddie Morgan had five each in an 18-inning game against the Philadelphia Athletics. ... The Blue Jays placed C Dioner Navarro on the family medical emergency list and optioned RHP Chad Jenkins to Triple-A Buffalo. Toronto recalled C Erik Kratz and Wagner from Triple-A. ... Indians RHP Danny Salazar (1-3) faces LHP J.A. Happ (1-1) in Thursday's series finale.