Goodrum, a rookie utility player, hit a two-run shot off Cleveland starter Carlos Carrasco and added a three-run blast. Goodrum doubled his homer total for the season.
Jose Iglesias had two hits and a run, and John Hicks scored twice for Detroit, which has won three of its past four. The Tigers had lost their past 11 games to their division rival.
Mike Fiers (4-2) held the Indians to one run on three hits with five strikeouts in six innings.
The Tigers placed third baseman Jeimer Candelario on the 10-day disabled list earlier in the day due to left wrist tendinitis. Right fielder Nicholas Castellanos missed his second consecutive game with a finger contusion after being hit by a pitch Saturday.
Carrasco (5-2), who was 7-1 over the past three seasons against Detroit, allowed three runs on six hits in 6 2/3 innings. Jose Ramirez homered and scored twice for the Indians.
Cleveland center fielder Bradley Zimmer sat for the fourth straight game with a chest injury.
Ramirez put the Indians on the board in the first with his two-out homer to right, his 13th of the year.
The first two Tigers batters in the third reached on singles, and Pete Kozma's one-out grounder brought home Iglesias.
Hicks led off the bottom of the fourth with a double. After a flyout, Goodrum smoked his first long ball of the game over the right-center-field wall.
Cleveland scored an unearned run against Joe Jimenez in the eighth. Ramirez reached on a Dixon Machado error with two outs, and Edwin Encarnacion brought him home with a double to right. Daniel Stumpf came in and retired Yonder Alonso on a short fly to keep the score 3-2.
Goodrum put the game away with his second homer in the bottom of the eighth. Evan Marshall issued walks to James McCann and Hicks. Following a strikeout, Goodrum crushed a 3-2 pitch from Zach McAllister over the right field fence.
Francisco Lindor's RBI single in the ninth completed the scoring.
--Field Level Media
Cleveland | Detroit | |
Carlos Carrasco | Player | Mike Fiers |
Loss | W/L | Win |
6.2 | IP | 6.0 |
4 | Strikeouts | 5 |
6 | Hits | 3 |
4.05 | ERA | 1.50 |
Cleveland | Detroit | |
Greg Allen | Player | Jose Iglesias |
3 | Hits | 2 |
0 | RBI | 0 |
0 | HR | 0 |
5 | TB | 3 |
.750 | Avg | .667 |