Kansas City trailed 1-0 until Mondesi's third-inning house run off Nick Pivetta (6-3), Mondesi's fourth home run in nine matches this year.
"That ball was far ball because you'll see struck," Royals manager Mike Matheny said. "He is a difference maker, and it is interesting to see."
In front of a season-high audience of 29,870 in Kauffman Stadium, Kris Bubic (2-2) won despite allowing two runs and five hits in 2 2/3 innings. Greg Holland pitched a perfect ninth for his fourth save, and also the Royals ceased their six-game losing series.
"Each of these is, but they are a fantastic team."
Boston's Christian Arroyo was ejected by plate umpire Jim Wolf afterwards that he took a called third strike for the next from the ninth to a pitch which Arroyo believed was indoors.
Whit Merrifield had his fourth consecutive multi-hit match, including an RBI double in the fifth which fostered Kansas City's lead to 4-2.
Boston confronted Kansas City for the first time because working outfielder Andrew Benintendi into the Royals on Feb. 10 within a three-team trade. Benintendi is overlooking the string due to a broken rib.
Kansas City utilized an opener for the first time this year, and Kyle Zimmer allowed three hits in two scoreless innings.
"Coming to the afternoon, there was some situations shared," Bubic explained. "I just tried to remain prepared and ready to get a normal beginning. I tried to only think 1 inning at a time."
He's 0-3 in four starts after beginning the season 6-0.
"We simply have to flip the page and attempt to tie the series tomorrow," Red Sox manager Alex Cora explained.
Alex Verdugo's RBI single put Boston ahead in the next, and J.D. Martinez struck a run-scoring only in the fifth which shut the Red Sox into 3-2.
Rafael Devers hit his 17th homer, a solo drive in off the eighth Scott Barlow, who hadn't allowed a home run in 38 innings.
Royals: OF Edward Olivares was optioned into Triple-A Omaha. The Royals chosen the contract of RHP Anthony Swarzak from Omaha and moved RHP Ronald Bolanos in the 10-day into the 60-day IL.