Gibson (11-10) takes on Cleveland right-hander Corey Kluber (14-9) in the opener, while Nolasco (5-10) squares off with Indians left-hander T.J. House (2-3) in the second game.
Gibson and House were both slated to start Wednesday, but were bumped back by the outbreak of severe weather.
"Kyle has got great stuff, but he tends to get stuck in a long inning every time he pitches," Minnesota manager Ron Gardenhire said. "He's got a great breaking ball and a good changeup that he can rely on. He just needs to learn to relax and not worry about the situation because his pitch counts tend to pile up in a hurry."
Though Gibson's season ERA is 4.27 over 28 starts, he has been brilliant in two outings at Progressive Field. He allowed one run in five innings to earn the win on April 5, then tossed seven scoreless frames in a May 5 no-decision.
The 6-foot-6, 207-pounder has struggled of late, posting his last victory on August 13, while going 0-1 with a 6.14 ERA over his last four starts.
Gardenhire believes Gibson may be wearing down after pitching a career-high 156 innings. He previous best was 152 2/3, split between the Twins and Triple-A Rochester in 2013.
"In terms of innings, Kyle is in an area code that he's never been in before," the skipper said. "Believe me, we're aware of that and watching it closely, as we are with all the guys. But we want Kyle to make the most of these opportunities because he's got to figure it out."
Nolasco went five innings and allowed two earned runs in his last start, taking a no-decision against the Angels on September 9. In his most recent game against Cleveland, he gave up four runs in 6 2/3 innings and took the loss at home on August 20.
Minnesota will be playing its fourth doubleheader of the year, but the other three were day/night affairs at Target Field that are officially considered individual games. The Twins swept Toronto on April 17, dropped two against the Dodgers on May 1 and split with Detroit on August 23.
This is the first time in Progressive Field history that the Indians will host three traditional doubleheaders in a season. Cleveland began playing at the downtown ballpark, then named Jacobs Field, in 1994.