The Royals' elimination number for the American League Wild Card remained at 1.
Mondesi led off the inning with a walk from Twins reliever Tommy Milone. Mondesi stole second, and went to third on a sacrifice bunt. The Twins opted to walk Whit Merrifield and Eric Hosmer, loading the bases with one out.
Burns, who came on in the ninth as a pinch-runner for Kendrys Morales, ripped a 1-1 pitch from Milone to center, deep enough to score the speedy Mondesi. It was Burns' first RBI with the Royals after being traded to Kansas City at the non-waiver Trade Deadline.
"I was on deck and saw they were putting Hosmer on," Burns said. "All that was on my mind, I'd seen [Milone] when I was with the A's, and I knew he was a good pitcher who could put it wherever he wants. I just wanted to stay middle and not try to pull it. I was very confident if I got it to the outfield, Mondi would score."
Added Royals manager Ned Yost: "I told Mondi, 'If you get on, we'll win it here.' He worked the count and did a great job of stealing second. … And then we felt good with Billy batting right-handed that he would put it in play."
Royals right-hander Ian Kennedy made it through five innings, giving up five hits and three runs while walking three and striking out five. He threw 106 pitches, 65 for strikes.
Twins rookie Jose Berrios, who came into the game with an 8.88 ERA, had his second straight serviceable outing: 4 2/3 innings, four hits, three runs, one walk.
"I felt good and I felt confident," Berrios said. "I think the work in the bullpens leading into the starts has been good. I think it's helped a lot."
MOMENTS THAT MATTERED Going down under: Royals right-handed reliever Peter Moylan, an Australian, got the Royals out of a big jam in the top of the sixth. Lefty Scott Alexander started the inning and gave up two singles while also committing a throwing error, setting the Twins up with runners on second and third and one out in a 3-3 game. But Moylan got rookie Byron Buxton to chase a slider in the dirt for a strikeout. Moylan then got James Beresford to roll out to third ending the threat.
"My mindset doesn't change because you always want to get outs," Moylan said. "But with a guy on third I pretty much knew I had to strike out Byron Buxton. Then I was able to get a fellow Aussie in James Beresford to ground out, so it worked out pretty well."
The Royals' bullpen put up six shutout innings.
"Tremendous job by the bullpen," Yost said. "They held the fort until we could score."
Escobar makes a splash:Eduardo Escobar ended a streak of 111 at-bats without a homer with his solo blast in the second. It was crushed into the fountain in right field, going a projected 448 feet, per Statcast™. It also had an exit velocity of 107 mph. It was Escobar's sixth of the year and his first since Aug. 2.
No. 101: Hosmer already established a career highs in home runs and RBIs earlier this month. On Saturday, Hosmer belted his 24th homer, a three-run shot that gave him 100 RBIs. Hosmer was back at it Tuesday, dropping a single into center in the fourth inning, scoring Jarrod Dyson for his 101st RBI.
Berrios lifted early: After giving up a two-out infield single to Cheslor Cuthbert to put runners at the corners with two outs in the fifth, Twins manager Paul Molitor opted to take Berrios -- who had only thrown 77 pitches -- out of the game. He brought in lefty Buddy Boshers, who promptly gave up a game-tying RBI single to Dyson, with the run getting charged to Berrios. Molitor said he decided to lift Berrios because the youngster was having trouble with his command, though he had mostly gotten away with it to that point.
"The results were good, but when you're watching him, you're seeing what's working and what's not working," Molitor said. "My feeling was that it was time to make a change."
The Twins unsuccessfully challenged a play in the eighth, when Terrance Gore was ruled safe by umpire Todd Tichenor on a stolen base attempt at third base. The call was ruled to stand after review, though Gore was quickly doubled off at third when Merrifield popped up a suicide squeeze attempt.
WHAT'S NEXT Twins: Right-hander Ervin Santana (7-11, 3.38 ERA) will make his final start of the season against his former team on Wednesday at 6:15 p.m. CT at Kauffman Stadium. Santana was given the option to shut it down this year, but he will make his 30th start of the year. He has a 2.35 ERA over his last 17 starts.
Royals: Left-hander Jason Vargas (0-0, 3.86 ERA) gets the start in the second game of the series against the Twins. Vargas, in his second start back from rehabbing from Tommy John surgery, gave up two runs in the first inning to Cleveland last Tuesday.