House (1-2) scattered nine hits, struck out three and didn't walk a batter. The rookie left-hander was making the eighth appearance, and seventh start, of his career.
Michael Brantley had three hits, including an RBI single in the eighth, for Cleveland.
House gave up a run in the first, another in the sixth and Danny Valencia hit a leadoff homer in the seventh. But House retired the next two hitters then was pulled after throwing 87 pitches.
Kansas City loaded the bases with no outs in the ninth against closer Cody Allen, pitching in a non-save situation. Allen struck out Lorenzo Cain on a 3-2 pitch before Eric Hosmer bounced into a game-ending double play.
House, taken in the 16th round of the 2008 draft, began the season at Triple-A Columbus. He made five starts with the Indians from May 23-June 14 before being sent back to the minors. He was recalled a week ago and lost to Seattle on Sunday against Felix Hernandez, a game in which the Indians were held to one hit.
Hosmer's RBI groundout in the first gave Kansas City the lead. Cain led off with a double and stole third before scoring.
Bourn's third homer of the season tied the game. Jason Kipnis gave Cleveland the lead with an RBI double and Lonnie Chisenhall added a run-scoring single.
Bourn's defense gave House a boost in the fifth. Billy Butler started the inning with a single, but was thrown out by Bourn trying to advance to third on Valencia's single to center.
Kansas City added a run in the sixth, but House struck out Butler with two runners on to end the inning.
Cleveland loaded the bases with no outs in the fifth before Swisher, who was batting .193 and struck out in his first two at-bats, lined a 1-2 pitch to right-center. The hit pushed the lead to 5-1 and gave Guthrie his shortest outing of the season. The right-hander was charged with six runs and allowed a season-high 11 hits in four-plus innings.
Guthrie had won his last three decisions and lost for the first time since June 6.
Chisenhall was 2 for 3 and raised his batting average to .342, but he doesn't have enough plate appearances to be listed among the league leaders. Cleveland's third baseman is making a strong push to be named to the American League All-Star team, which will be announced Sunday. Chisenhall is hitting .350 (55 for 157) with nine homers and 36 RBIs in 44 games since May 14.
Royals second baseman Omar Infante, who had two hits and an RBI, returned to the lineup after being a late scratch Friday because of tightness in his lower back.
NOTES: Swisher has been taking fly balls in right field during pregame drills. He appeared in 27 games in the outfield in 2013, but has yet to play there this season. ... Royals OF Nori Aoki (strained left groin) was eligible to come off the 15-day DL on Saturday, but will be sent on a rehab assignment in the next couple of days. Aoki, who is hitting .263, has been sidelined since June 21. ... Indians C Yan Gomes, who started 70 of the first 85 games, was given the night off as George Kottaras started behind the plate. ... Royals OF Alex Gordon snapped an 0-for-16 slump with a sixth-inning single. ... Royals LHP Danny Duffy (5-7) takes on RHP Corey Kluber (7-6) in the three-game series finale Sunday.