Victor Martinez drove in three runs, Kelly finished 3-for-5 with two runs scored and Austin Jackson also scored twice for the Tigers, who finished the road portion of their 2011 schedule with a mark of 45-36.
"This was a very long road trip, a 10-day road trip. We went 6-3, so that's pretty good at any time of the year," Tigers catcher Alex Avila said.
Billy Butler and Jeff Francoeur both drove in a run for the Royals, who went 40-41 at home this season. Felipe Paulino lasted five innings and surrendered two runs on six hits while Kelvin Herrera (0-1) got the loss in his first big league appearance as he gave up three runs in the eighth inning.
A Martinez RBI single in the top of the first staked Detroit to an early lead, but Butler and Francoeur both had RBI doubles in the bottom of the frame to give the Royals a 2-1 advantage.
Martinez again helped the Tigers in the seventh as his RBI single scored Kelly, who had doubled earlier in the inning, to tie the contest.
In the eighth, the Tigers went ahead for good. With Herrera on the mound, Raburn was hit by a pitch and Miguel Cabrera followed with a pinch-hit double to give Detroit the lead. Later in the frame, Kelly hit his sixth home run of the season for a 6-3 lead.
"We've played our butts off in the month of September," Francoeur said. "The Tigers are playing for home field advantage and you can tell how much it meant to them when you bring in Miguel (Cabrera) to hit like that."
After Fister pitched a 1-2-3 eighth, Jose Valverde came on in the ninth to close the game, but got into some trouble.
Eric Hosmer led off with a single and moved to second on a passed ball. After Francoeur struck out, Mike Moustakas singled to bring the tying run to the plate. Valverde, though, got Brayan Pena to pop out and Salvador Perez to foul out for his MLB-leading 47th save of the season.
Detroit won 11 of 18 games against Kansas City this season...Detroit, which has already clinched the AL Central, closes out the regular season at home with a four-game set against Baltimore followed by a three-game series against Cleveland...Kansas City plays three-game series in Chicago and Minnesota to finish the season.