Clarkin, the No. 7 prospect in the Yankees organization, threw 39 of 63 pitches for strikes and earned the win after allowing two runs in four innings.
Meanwhile, Profar went 2-for-5 with a homer and three RBIs.
"I think I had a slow week last week, I was a little bit late," Profar said. "So this week my approach is just to be early and see the ball and hit the ball."
Surprise used a trio of big innings to capture the win, as the club scored three runs in the fourth, fifth and eighth innings.
The first of those crooked numbers was courtesy of Profar as he blasted a three-run homer 415 feet to left field that gave Surprise an early 4-2 lead.
"It's very good. We're facing a lot of good pitchers that have good pitches," Profar said of the AFL. "They're going to be in the big leagues, they're good, so it's good for me to compete against them."
Once regarded as the best prospect in all of baseball, Profar's career has not gone nearly as planned.
The infielder made his Major League debut in '13 and was expected to become an everyday player the next year, but missed the entire year after he tore a muscle in his shoulder.
Rehab was slow and Profar ultimately had surgery in February, which sidelined him for the bulk of this year as well.
"Just been working hard to be in this position," Profar said. "I'm getting better every day and I'm here now."
The 22-year old appeared in 12 games at the end of this season and has played in another 13 so far in the Arizona Fall League. Profar is hitting .260, but said he's not worried about results and that it's simply "good to be playing."
While Profar enjoys being back on a baseball field, he has been serving as a designated hitter and admittedly gets a bit restless on the bench.
Profar spent the bulk of Tuesday's game on the top step of the dugout and would work on his swing from that spot in between batters.
"I don't like it," Profar said of not playing the field. "But it is what it is, I'm getting at-bats to be ready for next year. I'll be patient."