Austin Jackson singled to lead off the first inning and after Torii Hunter popped out, Cabrera belted the first pitch he saw from Royals starter Bruce Chen into the left-field seats for a quick 2-0 lead.
The 2012 Triple Crown winner added a run-scoring single in the third, finishing 2-for-3 to raise his MLB-best batting average to .360 while boosting his RBI total to 120, also the best in baseball.
Scherzer yielded two runs on five hits, didn't issue a walk and struck out four for the American League Central-leading Tigers, who took 3-of-5 games against the Royals.
Chen (5-1) was tagged for six runs on eight hits in a 5 1/3-inning effort.
Billy Butler went 2-for-4 with a solo homer and two runs scored for Kansas City.