Adalberto Mondesi homered for the Royals and Whit Merrifield had three hits, including a pair of doubles.
A quartet of relievers combined for 3 2/3 scoreless innings. Jake Brentz (4-2) struck out two in the seventh, Josh Staumont worked out of a jam in the eighth and Scott Barlow finished for his 12th save.
Byron Buxton had two of Minnesota's six hits.
Isbel's single off Jorge Alcala (3-6) got just past diving second baseman Luis Arraez and rolled into right field to score pinch-runner Hunter Dozier.
Isbel was called up Sunday morning from Triple-A Omaha - playing this weekend a few miles away in St. Paul - when outfielder Michael A. Taylor was placed on the family medical emergency list. Isbel had been in the minors since April 21.
''It was hectic morning, but it was awesome,'' said Isbel, who took about a 25-minute Uber ride to Target Field. ''But I couldn't find the entrance to the park. ... I think I went around the stadium probably five times.''
''Not long after we got here, he was in the clubhouse,'' manager Mike Matheny said.
Minnesota had two runners on in the eighth, but Miguel Sano hit into an inning-ending double play. He also struck out three times.
Brent Rooker delivered a two-out, two-run double for the Twins to tie it 3-3 in the sixth.
''It was kind of a game where we hung around, we kept it close enough for it to be a good, tight ballgame. We didn't do it by pitching and playing a great ballgame,'' Twins manager Rocco Baldelli said.
Minnesota starter Bailey Ober allowed three earned runs in 4 1/3 innings while striking out six. It was his 10th straight start allowing three earned runs or fewer, but he has completed six innings in just two of those outings.
''I felt like I was able to throw some pretty good off-speed pitches today and get them to chase out of the zone,'' Ober said.
Ober, who has tossed a career-high 99 innings between the Twins and Triple-A this season, retired nine straight Royals before a pair of fifth-inning singles ended his day.
He was replaced by Jovani Moran, who made his major league debut. Merrifield blooped the left-hander's first pitch down the right-field line for an RBI double and a 3-1 lead.
Mondesi snapped an 0-for-17 stretch with a second-inning homer to put the Royals up 2-1.
Kansas City starter Kris Bubic allowed three runs, two earned, in 5 1/3 innings.
Andrew Benintendi's ninth-inning sacrifice fly was his 14th RBI of Kansas City's seven-game trip, tying the franchise mark for RBIs on a trip of seven games or fewer.
WAIT A MINUTE
Kansas City thought it had turned an inning-ending 4-5-6 double play in the third. With one out, a softly hit ball bounced in front of Merrifield behind second base, who lobbed it to third to force Andrelton Simmons. A throw back to second forced out Buxton.
However, as the Royals left the field, Baldelli successfully challenged that an infield fly should have been called. Matheny came out for a lengthy discussion of the change. Upon video review, the infield fly call stood.
Merrifield acknowledged he let the ball drop - something he did successfully in a 2019 game at Detroit.
''I'm always looking to find ways to get cheap outs for our pitchers. Wish the umpires would have handled it a little different, but credit to them for admitting they dropped the ball on that one,'' he said.
Twins: Rooker is going on the paternity list awaiting the birth of his first child.
Royals: Begin a three-game home series against Oakland on Tuesday with RHP Jackson Kowar (0-3, 9.53 ERA) facing RHP Frankie Montas (12-9, 3.57) of the A's.
Twins: Travel to the Bronx Monday to make up a Aug. 22 rainout against the Yankees. John Gant (5-9, 3.78) is to pitch against New York's Luis Gil (1-0, 1.42).
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