Santana hit a solo home run with one out in the eighth inning, leading the Indians to a 1-0 victory over the Oakland Athletics in the opener of a three-game series.
Right-hander Carlos Carrasco (9-6) pitched eight shutout innings, allowing just four hits, helping the Indians win for the ninth time in 12 games.
"The way those guys were pitching tonight," Indians manager Terry Francona said of Carrasco and Oakland's Andrew Triggs, "it looked like (a home run) was the way somebody was going to have to score."
Carrasco and Triggs had dueling shutouts until the A's rookie was pulled after a season-high six innings, having allowed just three hits.
Right-hander Liam Hendriks pitched out of a second-and-third jam in the seventh before turning the ball over the righty Ryan Dull to start the eighth.
Santana jumped on Dull's ninth pitch for his 27th homer of the season, a monster shot just inside the right field foul pole.
"I thought maybe foul," Santana said of his initial reaction to the ball that nearly reached the second deck in the spacious Oakland stadium. "I was very happy (when it was fair)."
The home run was Santana's team-leading 13th on the road.
He matched his career high for a season, but that was not what he had in mind when he went to the plate with one out and nobody on base late in a tie game.
"I was not thinking home run. Just try to get on base," he said. "We need runs."
Dull (5-4) had allowed only one previous home run this season in 56 games.
"You feel for him," A's manager Bob Melvin said of Triggs, who was vying for his first major league win. "You can't help but pull for a guy who's a great team guy."
Carrasco, who had allowed at least three runs in each of his past five starts dating back to July 27, struck out nine and did not walk a batter.
"The way I pitched today," he said, "that's the way I feel I can pitch all the time."
Left-hander Andrew Miller struck out the side in the ninth for his 11th save, his second as an Indian.
The combined shutout was Carrasco's second of the season.
Among the batters Miller retired was Valencia, who didn't start for the second consecutive game. He struck out as a pinch hitter with one out in the ninth.
Lonnie Chisenhall had two hits, including a double, for the Indians, who were opening a seven-game trip.
Jason Kipnis also doubled for Cleveland, which beat Oakland for the fourth consecutive time and clinched the season series.
The Indians out-hit the A's 7-4.
Ryon Healy had two of Oakland's hits.
Coco Crisp had a double for the A's, who were opening a three-game homestand. The fact that it wasn't a triple might have cost the A's the game.
With the score tied in the sixth, Crisp was thrown out trying to stretch his hit to the fence in right field into a triple.
The A's challenged the call, but it was upheld upon review.
"That was a bang-bang play," Francona said. "It's probably one of those plays where if they call him safe, the call stands."
Melvin didn't like the call.
"I thought he was safe," the Oakland manager said. "The evidence has to show you conclusively, and that probably fell under the one where they couldn't (see) for sure. I might be a little biased, but I thought he was safe."
Triggs struck out six and walked just one in his six innings.
"I actually felt pretty good," Triggs said of his 89-pitch outing. "My arm felt good. My legs maybe got a little wobbly, but I felt a lot better than even I would've anticipated."
NOTES: The Indians have played five consecutive one-run games, and they won four of them. ... The shutout was Cleveland's ninth of the season. ... Before the game, the A's announced that 1B/3B Danny Valencia and DH Billy Butler were fined, but not suspended, for their fight in the clubhouse before Friday's win at Texas. The scuffle reportedly was over a comment Butler made when Valencia was speaking with an equipment company representative. ... Butler, who was injured in the fight, was placed on the seven-day concussion disabled list Monday. ... The A's also played without SS Marcus Semien, who was with his wife for the birth of their child. ... The A's recalled INF Arismendy Alcantara from Triple-A Nashville to replace Butler on the active roster. ... Indians C Yan Gomes (separated right shoulder) threw from 90 feet before the game, after which manager Terry Francona said he could be sent on a rehab assignment in the minors by the end of the month.