Mauer's bases-loaded blast -- the first by a Twin this season -- came in the second inning and put Minnesota ahead 8-2.
Chris Parmalee had cracked a three-run shot in the first inning.
But Minnesota starter Liam Hendricks surrendered five runs (three earned) on 10 hits in just 3 2/3 innings and had to be lifted in favor of Anthony Swarzak (3-4), who registered the win despite yielding two runs over 2 2/3 frames.
The Twins bullpen closed the door after that, however, blanking the Royals over the final 2 2/3 innings with Glen Perkins firing a 1-2-3 ninth for his 10th save.
Perkins also saved the first game of the doubleheader, which the Twins won 3-1.
Royals starter Luke Hochevar (7-13) was rocked for eight runs on six hits, lasting just 1 2/3 innings.
Salvador Perez went 4-for-5 with an RBI while Billy Butler added three hits, including an RBI single, for Kansas City.