That's when Encarnacion drilled the first pitch he saw from Glasnow 404 feet over the wall in center field for his 29th home run, breaking a scoreless tie and giving Indians starter Corey Kluber a shot at his major league-leading 17th win.
Encarnacion was aggressive against Glasnow's fastball in his first two at-bats, but he went looking for an offspeed pitch his third time up and didn't miss it.
"After I had good contact in the first two at-bats, I was ready for the breaking ball," Encarnacion said.
Cleveland added two runs in the eighth when Greg Allen scored on a wild pitch and Michael Brantley singled home Francisco Lindor before Brad Hand to closed the door on the Rays in the ninth for a 3-0 Tribe victory.
Embattled reliever Cody Allen picked up Kluber with a perfect eighth inning, striking out Tampa shortstop Willy Adames and pinch hitter Brandon Lowe. Allen, who blew a save on Wednesday, was making his third straight appearance for Cleveland, but Indians manager Terry Francona said he thought Allen was efficient and threw his breaking ball well.
"I thought he looked tremendous," Francona said. "He's gotten to a good place, now we've got to keep him there."
Glasnow (0-2, 3.95) appeared unhittable through 6 1/3 innings. He hit Greg Allen with a pitch in the sixth, but retired the next two batters to get out of trouble before surrendering Encarnacion's blast in the next frame.
"I think our guys were just trying to see the one that was straight before they get in a hole, because that's pretty special stuff," Francona said.
Kluber (17-7, 2.80) matched Glasnow's brilliance with seven shutout innings of his own, allowing just two hits and striking out eight with two walks. He labored through the first inning after giving up a leadoff hit to Joey Wendle and a walk to Matt Duffy. He struck out Ji-Man Choi and got Tommy Pham to bounce into an inning-ending double play.
"You just try to flush it and kind of get back to what you'd like to do and try to find your delivery," Kluber said.
In the fourth, Choi reached on a walk with one out and Pham singled, but Kluber again escaped unscathed by striking out Jake Bauers on a filthy 3-2 comeback fastball and getting C.J. Cron on a fly ball to left.
Kluber retired the final 11 batters he faced after Pham's base hit and Francona said the two-time Cy Young Award winner looked "crisp."
"Even some of his two-seamers were what, 92, 93?" Francona said. "His breaking ball was better. I thought he was really good."
Indians hitters started going after Glasnow's fastball early in the count the second time through the order, but the results did not change until Melky Cabrera bounced a single past shortstop with two outs in the fifth for Cleveland's first hit.
Greg Allen's two-out single in the eighth sparked a two-run rally that provided some insurance runs against Rays reliever Ryne Stanek. Allen stole second and advanced to third on a wild pitch before scoring on another wild pitch with Michael Brantley at the plate.
Lindor, who walked after Allen's base hit, stole second and third and trotted home on Brantley's base hit past the mound. It was Brantley's 70th RBI, giving Cleveland five hitters with at least 70 this season.
What it means
Cleveland improves to 94-58 all time against the Rays. The Tribe's magic number to clinch a third consecutive division title is down to 15 with 28 games remaining.
In the chase for the No. 2 seed in the American League playoffs, and home field advantage in the Division Series, the Indians trail Houston by 5.5 games. The Astros were playing the Angels on Friday at 8 p.m.
Glasnow threw 79 pitches, 56 (71 percent) for strikes. Kluber threw 109 pitches, 70 (64 percent) for strikes.
Thanks for coming
The Rays and Indians drew 25,639 to Progressive Field on Friday night. First pitch was at 7:10 p.m. with a temperature of 76 degrees.
Right-hander Shane Bieber (8-2, 4.52) will start Saturday night for the Indians as Tampa Bay counters with lefty Blake Snell (16-5, 2.05) at 7:10 p.m.
FS1, WTAM and WMMS will carry the game.
Bieber will be making his first career start against the Rays. Snell is 0-1 with a 2.08 ERA in two previous starts against the Indians.