The Royals starter gave up two homers to Alex Avila as the Tigers edged Kansas City 3-2 in the series finale. The loss drops the Royals (78-71) back to 3 1/2 games behind Tampa Bay and Texas for an American League Wild Card spot.
Avila's homers were his 10th and 11th of the season, both of which gave Detroit (86-63) the lead. The first, a two-run shot, opened the scoring in the second inning.
Alex Gordon responded with his 20th homer of the year in the fourth frame to cut the lead in half.
Alcides Escobar scored from third on a wild pitch by Drew Smyly in the eighth to tie it.
Smyly (6-0) earned the win with a single inning of relief despite giving up the tying tally. Max Scherzer struck out 12 batters through five innings in the start.
Guthrie (14-11) struck out four and surrendered 13 hits while pitching all eight of Kansas City's innings.
The Royals return home Monday to begin a series with division foe Cleveland, who are a half-game back of a Wild Card spot.