Austin Jackson drove in four runs as the Tigers finished with a season-high 26 hits. Dirks, who is hitting .410 against Kansas City this season, scored four times.
Infante had run-producing singles in the second, fourth and seventh innings and a three-run double in the fifth. It was more than enough support for Anibal Sanchez (13-7), who allowed one run in seven innings while lowering his AL-best ERA to 2.61.
Sparked by the return of Miguel Cabrera, every Detroit starter had a hit and scored a run in the first five innings. The Tigers sent 10 men to the plate in the second and fourth, scoring five times in each frame.
Cabrera, who did not play in four of the previous five games because of an abdominal strain, went 1 for 2 with a RBI and walked twice before being replaced by Danny Worth in the sixth inning.
Much of Detroit's onslaught came against James Shields, who was knocked out in the fourth inning in one of the worst starts of his career.
Jackson had a two-run double in the second and a two-run single in the fourth. The four RBIs matched his career high.
Shields (10-9), who was 4-0 in his previous five starts, was charged with 10 runs and 14 hits in 3 2-3 innings in his shortest start of the season. The runs and hits matched career-worst totals for the right-hander.
The last team to collect 14 hits against Shields was the Tigers on June 28, 2012, in 7 2-3 innings.
Billy Butler drove in the first Royals run with a single in the first for his sixth straight hit. David Lough doubled and scored on Jarrod Dyson's sacrifice fly in the ninth for the other Kansas City run.
NOTES: Royals C Salvador Perez was cleared to play after experiencing dizziness Thursday and leaving in the fifth inning after taking a foul tip off the mask. Perez, who was on the concussion list in August, switched to a new mask. ``We're going to scoot him up under the hitters a little closer, see if maybe he can dodge some foul balls that way,'' Royals manager Ned Yost said. ... SS Jose Iglesias was held out of the Tigers lineup after exiting in the fifth Wednesday with shin splints. ... Yost said 2B Chris Getz has not been cleared to return after suffering a possible concussion Tuesday. ... RHP Justin Verlander, who starts Saturday, is 0-2 with a 2.60 ERA in four 2012 starts against the Royals.