CLEVELAND -- The Detroit Tigers are already halfway to their win total against the Cleveland Indians from last year.

The Tigers were 4-14 vs. Central Division rival Cleveland last year, but 2-1 vs. the Indians over the weekend.

Alex Avila hit a two-run homer and Matthew Boyd pitched six strong innings as the Tigers beat Cleveland 4-1 on Sunday at Progressive Field.

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.

"We recognize what happened last year," said Tigers closer Francisco Rodriguez. "That's a team that competes all-around. We know we've got play our best against them."

The Tigers did that over the weekend, winning two of the three games in the series.

"They did their share of beating the Tigers last year, so it's good to win the first series this year," said Detroit manager Brad Ausmus.

It is the first series win for the Tigers over the Indians since June 22-24, 2015.

Boyd (2-1) gave up one run in six innings to get the win.

"His changeup was really good. It took the sting out of our bats and he could throw it at any time in any count," said Cleveland manager Terry Francona.

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.

Avila was 2-for-2 in the game, 4-for-5 in the series and is 7-for-10 for the season.

"He's swinging the bat well, and he was swinging the bat well before we got here," Ausmus said.

Cleveland cut the Detroit lead to 2-1 in the sixth inning. Michael Brantley and Edwin Encarnacion singled, then executed a double steal, putting runners at second and third with one out.

A sacrifice fly by Jose Ramirez drove in Brantley, but Boyd struck out Brandon Guyer to end the inning with the Tigers still leading 2-1.

"That was a big out for me to get because it was still 2-1 at the time," Boyd said. "This was a great team win for us. We had great defense and we got the hits when we needed to."

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.

"Those add-on runs late in the game are enormous. The later they are, the more valuable they are," Ausmus said. "It gives you some breathing room and your opponent has less outs."

Carrasco only gave up four hits and the two runs in 6 2/3 innings.

"Other than the fastball to Avila (that was hit for a home run), he was really good," Francona said. "He kept it right there and gave us a chance."

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.