Martinez's one-out shot over the center-field wall bailed out the Tigers, who had been unable to get a clutch hit for eight innings. But in the ninth, Torii Hunter drew a leadoff walk from Allen (5-4), Miguel Cabrera singled, and after Victor Martinez flied out, J.D. Martinez connected for his 19th homer, a crushing blow to the Indians.
Phil Coke (3-2) pitched 1 1-3 innings and Joe Nathan worked the ninth for his 29th save.
Detroit's comeback kept the Tigers on the heels of first-place Kansas City in the AL Central.
The Indians wasted a strong performance by Carlos Carrasco, who side-stepped danger for 5 1-3 innings and struck out a career-high 10.
Carlos Santana hit a two-run homer for Cleveland, which has dropped the first two in this critical four-game series.
J.D. Martinez has hit two homers in three career at-bats off Allen, who was trying to protect a 2-1 lead against the middle of Detroit's vaunted lineup.
Until Detroit's uprising, Carrasco was in line for his fourth straight win. The right-hander managed to work out of jams in four straight innings, making big pitches and keeping the Tigers' power hitters in the ballpark one night after Detroit slugged five homers and collected 20 hits.
Tigers rookie starter Kyle Lobstein was superb in his first career road start, allowing five hits in 5 1-3 innings and striking out 10.
Every time the Tigers threatened, Carrasco found a way out of trouble.
Clinging to a one-run lead in the fifth, he gave up a leadoff double to Cabrera, who went to third on Victor Martinez's single. Carrasco then struck out J.D. Martinez looking, fanned Nick Castellanos and locked up Alex Avila with an 84 mph off-speed pitch to end the inning, celebrating his 10th whiff with a demonstrative fist pump.
Even Cabrera patted Carrasco on the rear as the right-hander passed him while leaving the field.
After Carrasco gave up a one-out single in the sixth, manager Terry Francona pulled him and the 27-year-old received a rousing ovation from the appreciative crowd. Carrasco has a 0.90 ERA in his past five starts.
Santana got the Indians out of the gate fast, hitting his 23rd homer in the first. Michael Brantley singled with two outs before Santana connected for a shot into Detroit's bullpen in right.
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