Masterson yielded three hits over seven innings but Cleveland (3-2) did not score until plating two runs in the ninth of Monday's 2-0 victory at Oakland.
"It was a nice tone," he told the Indians' official website. "I think that's as good a tone as you can set."
Masterson is 3-6 with a 4.40 ERA in 16 career starts against Minnesota (2-3), going 1-0 with a 3.95 ERA in two last year. He went 8-4 with a 3.12 ERA in 16 home outings in 2013.
Nolasco, meanwhile, signed a deal worth $49 million over four years in the offseason. He yielded five runs - two homers - over six innings in Monday's 5-3 road defeat to the Chicago White Sox in his club debut.
"I thought I made a lot of good pitches, but I thought the difference in the game was throwing a couple of bad pitches," Nolasco told the Twins' official website.
The right-hander has never faced Cleveland.
Sunday's contest will be the first between these teams in which managers with 1,000 wins will square off.
That's because Minnesota's Ron Gardenhire reached the milestone in Saturday's 7-3 victory, becoming the 10th manager in history to win that many with the same club. The list includes managing immortals Connie Mack, John McGraw, Walter Alston, Tommy Lasorda and Earl Weaver.
''I haven't looked at the list,'' he said. ''I kind of stayed away from all that stuff. We were kinda talking about it earlier. I really haven't gotten into this very much: How many? Who? Maybe I'll look at it now.
''I guess you tip your hat to those guys because I know how hard it is.''
Terry Francona has also won 1,000 games and is with his third club.
''Gardy's been doing this for a long time,'' Francona said. ''Yeah, I guess I wish it would have come in the next series. But he's been good at what he does for a long time. I think that number indicates he's getting old.''
Masterson will try to add to the early woes of Joe Mauer, who is 8 for 35 against the Indians starter and 4 for 21 this year. Jason Kubel (3 for 17) has also fared poorly versus Masterson.
Chris Colabello, 7 for 18 with a team-high seven RBIs this year, has yet to face Masterson.
Minnesota outfielder Oswaldo Arcia's status is uncertain after he sat out Saturday with a sore wrist.
Cleveland's Jason Kipnis, who signed a $52.5 million, six-year contract Friday, batted .427 with four homers and 24 RBIs against Minnesota last season, but is 3 for 17 in the first week.
He's drawn four walks in this series while going hitless in four official at-bats.