Encarnacion and leadoff hitter Francisco Lindor each hit his 17th homer of the season. Jose Ramirez walked four times and scored twice.
Rookie Shane Bieber (2-0) handcuffed the Tigers through seven innings, allowing just four hits and a walk while striking out a career-best nine in his third major league start.
Zach McAllister and George Kontos each threw a scoreless inning to complete a five-hitter.
Detroit starter Mike Fiers (5-4) gave up four runs on four hits over five innings.
The American League Central Division-leading Indians continued their dominance over their division rival. They have won eight of the first 11 games of the season series. Detroit has scored two or fewer runs in seven of those matchups.
Bieber struck out two batters in the first, then upped the ante by striking out the side in the second.
Lindor opened the scoring with two outs in the third inning when he blasted a 90 mph fastball from Fiers over the right field wall.
Cleveland made it 3-0 in the fourth inning. Fiers walked Ramirez, and Encarnacion followed with his blast over the left field wall.
Detroit had two baserunners with one out in the fifth, but Jose Iglesias hit into a fielder's choice and JaCoby Jones struck out.
The Indians pushed across another run in the fifth. Tyler Naquin reached on a wild pitch after striking out. One out later, Michael Brantley drilled a double to right-center, and Naquin scored from first.
Alonso's 12th homer of the season capped a five-run seventh. Naquin got the big inning started with a single, and Lindor then walked. A wild pitch advanced both runners and, one out later, Ramirez was intentionally walked.
Encarnacion brought in the first run of the inning with a single before Johnny Barbato served up Alonso's slam to right-center.
Cleveland's 10th run scored on an eighth-inning error after Jason Kipnis led off with a double.
--Field Level Media
Detroit | Cleveland | |
Mike Fiers | Player | Shane Bieber |
Loss | W/L | Win |
5.0 | IP | 7.0 |
4 | Strikeouts | 9 |
4 | Hits | 4 |
7.20 | ERA | 0.00 |
Detroit | Cleveland | |
Nicholas Castellanos | Player | Yonder Alonso |
1 | Hits | 2 |
0 | RBI | 4 |
0 | HR | 1 |
1 | TB | 5 |
.333 | Avg | .500 |