Guthrie (3-3) gave up 10 hits, but did not walk a batter and allowed only an eighth-inning run.
Detroit left at least two runners on against Guthrie in three different innings and on another occasion failed to score after producing a leadoff double.
The inability to come through with a clutch hit plagued the Tigers all the way into the ninth inning, when Kelvin Herrera came on in relief.
Detroit put runners on first and second with one away, but Herrera got Miguel Cabrera to ground into a game-ending double play for the first save of his career.
Johnny Giavotella drove in a Kansas City run in the fifth with a fielder's choice grounder and Alex Gordon hit a mammoth home run in the sixth.
The loss went to Rick Porcello (9-10), who allowed both runs on eight hits in five innings.
Detroit has dropped four out of six and missed a chance to gain ground on the American League Central leading Chicago White Sox, who lost earlier in the day at Baltimore. Chicago remains three games in front of the Tigers.