Harrison was supposed to start on Sunday, but he was roughed up in his last two starts, and manager Ron Washington decided to give him the extra time.
Harrison will be opposed by right-hander Ubaldo Jimenez, who is 9-15 with a 5.58 ERA in his first full season with the Indians.
Harrison, 15-9 with a 3.37 ERA in his second full season in the Rangers' rotation, benefited from a similar rest late last season.
He is coming off back-to-back losses, to the Royals and Rays, in which he pitched a combined 10 innings and allowed 10 earned runs, along with two unearned.
"We're just trying to give [Harrison] an extra couple of days," Washington said. "He understands that last year we gave him a break and it helped him. He's the only one that's been on regular terms, so we're going to do it right now and see where it takes us."
Harrison was not turning cartwheels over the prospect of getting the extra rest, but he seemed to understand.
"I'm definitely going to feel the difference pitching Tuesday," he said on Sunday. "I would have stayed on the regular five days. Right now it feels like the regular start date."
Harrison threw in the bullpen on Saturday and said the session went well.
"It went good. Threw 60 pitches," he said. "I just threw a long one. I had a couple extra days to recover."
Pitching against Cleveland might turn out to be a blessing in disguise for Harrison and Texas.
The Indians feature a left-handed-heavy lineup, and conventional wisdom would suggest that Harrison, a lefty, would fare better.
It also sets him up to pitch against Seattle in the following series, a team against which he's done well.
"That just happened to fall like that," Washington said.
Jimenez will be making his 29th start of the season. He is 1-8 since the All-Star break but is coming off a strong -- albeit losing -- performance in his most recent outing.
He worked 7 1/3 innings against the Tigers on Wednesday, giving up six hits and four earned runs in a 7-1 Indians loss.
"That's part of how everything's going for me right now," Jimenez said. "When I pitch bad, I lose the game. Sometimes pitching good or one mistake, one pitch, one inning, I still lose the game. That's the way this year goes."
Indians: Chisenhall homers in return
Third baseman Lonnie Chisenhall played his first game since returning from the disabled list on Monday and hit a solo home run in the seventh inning. He was out of action for more than two months after being hit with a pitch on June 29 and suffering a broken forearm. Chisenhall started at third base and hit sixth, going 1-for-3 with the homer and a walk.
The Indians won't be heading to the postseason, but some players said that there is an importance in finishing out of last place.
"It's definitely important," said infielder Jason Donald. "You definitely don't want to finish the year and say we finished last in the Central. Some people will say it's not important unless you're finishing first. But I think there's a pride factor that comes in with it. We're certainly going to do everything that we can to battle it out until the end of the year."
Rangers: A winning road trip
The Rangers completed a 10-game road trip on Sunday, going 6-4, and are home for six games against the Indians and Mariners.
Outfielder Josh Hamilton is hitting .313 in his career against the Indians, with 10 home runs and 33 RBIs. He's 1-for-6 with three walks against Jimenez.
Hamilton has 40 home runs, making him the fifth Rangers player to hit that many in a season. The others are Juan Gonzalez (five times), Rafael Palmeiro (three), Alex Rodriguez (three) and Mark Teixeira (one).
Jimenez has made three career starts against Texas, posting a 1-1 record and a 4.58 ERA. He's allowed nine runs on 17 hits and 11 walks in 17 2/3 innings.