The Indians prospect allowed a run on four hits over 5 1/3 innings as Kinston beat the Frederick Keys, 3-1, in Game 1 of the Mills Cup Finals.
Cook (1-1) walked four and struck out five to earn his first postseason win. He exited after walking Miguel Abreu with one out in the sixth, having thrown around 90 pitches.
"That first inning, I came out and my fastball command wasn't really there and I had to rely on my changeup and curveball," Cook said. "My pitching coach, Mickey Callaway, came over and said I had been guiding my fastball in there and hoping it would go there instead of seeing the target and just letting it go there."
The 21-year-old right-hander had a solid regular season, going 9-9 with a 4.56 ERA in 25 Carolina League starts. The former ninth-round pick is one of several Indians who won the Midwest League championship last year with Class A Lake County.
"It's big. We have this playoff experience that we went through it last year," Cook said. "I'd 70-80 percent of the guys were on that team and they know what it takes to win a championship."
After Cook surrendered a one-run lead in the bottom of the third, Jesus Aguilar put him right back on top with a solo homer in the fourth.
"It's huge, you can't say enough," Cook said. "Not only did he put us ahead, but he sparked the rest of the club."
Seeking to bring the Mills Cup to Kinston for the first time since 2006, Cook said taking Game 1 of the best-of-5 series was a step in the right direction.
"Not only is it Game 1, but it's on the road," he said. "Guys came out and played real well. It's good to have that early momentum and, hopefully, we can keep it going."
Chris Jones took over for Cook and allowed one hit in a scoreless inning. Toru Marata tossed 1 1/3 scoreless frames and Preston Guilmet retired the final four batters to earn his second playoff save.
Manny Machado, the Orioles' top prospect, doubled home the Keys' only run in the third.
Frederick starter Nick Haughian (0-1) gave up all three runs -- one earned -- on six hits over four innings. He struck out four and walked one.