The Tigers won two of three games from the slumping Indians, who went 2-4 on their season-opening homestand. Cleveland has lost seven of its last nine games.
Boyd (2-1) gave up one run in six innings to get the win. Francisco Rodriguez pitched the ninth inning to pick up his fifth save. Cleveland starter Carlos Carrasco (1-1), who gave up two runs in 6 2/3 innings, took the loss.
Detroit took an early lead against Carrasco in the second inning. With two outs and nobody on base, Tyler Collins singled to left field. Avila then hit Carrasco's first pitch over the wall in center field for his second home run, giving the Tigers a 2-0 lead.
The Tigers added two runs in the eighth inning. Nick Castellanos led off with a double against reliever Bryan Shaw. Miguel Cabrera singled, scoring Castellanos to make it a 3-1 Detroit lead. Victor Martinez singled, moving Cabrera to second, but Cabrera then was removed from the game due to lower back tightness. He was replaced by pinch-runner Jacoby Jones.
Jones went to third when Justin Upton grounded into a double play, and Jones scored on a wild pitch by Zach McAllister, in relief of Shaw.
NOTES: Tigers RHP Michael Fulmer will start Monday night at Tampa Bay. In two starts last year against the Rays, Fulmer was 2-0 with a 0.64 ERA and 21 strikeouts in 14 innings. ... Detroit 1B Miguel Cabrera's next home run will be the 449th of his career, tying him with Jeff Bagwell and Vladimir Guerrero for 38th on the all-time list. ... Indians DH Carlos Santana hit his eighth career home run against RHP Justin Verlander on Saturday. That's the most homers off Verlander by any hitter in the majors. Despite the homers, Santana's career batting average against Verlander is just .217 (15-for-69). ... Indians' 2B Jose Ramirez's six RBIs on Saturday tied the club record for most RBI in a game by a second baseman, done six times previously, most recently by Duane Kuiper on July 27, 1978.