Cole threw 33 of his 53 pitches for strikes, giving up just two hits and a walk. The 21-year-old right-hander touched 100 mph six times and 101 once.
He retired Trout, MLB.com's top prospect, to start the game and worked around a two-out walk to fellow Angels prospect Hank Conger before striking out Boston's Will Middlebrooks to end the frame.
Harper (Nationals), the 2010 No. 1 overall pick and baseball's No. 2 prospect, led off in the second and lined a single to right field. The game marked the second straight in which Cole faced a fellow first overall pick -- he took on Tampa Bay's Tim Beckham (2008) in his pro debut.
"It was fun," Cole said. "You know why [Harper] was taken first overall. He was more patient than I expected. I threw a good 3-2 pitch, and he got a hit. There's nothing you can do about it."
Yet another first-rounder, San Francisco's Joe Panik, added a one-out single, but Cole came back to retire Zach Walters and Tyson Gillies to end the inning. He then worked a 1-2-3 third, retiring Trout, Brandon Crawford (Giants) and Conger to end his day.
"I had a strong fastball and change-up," Cole said. "I was pounding the fastball in there, trying to stay aggressive even if I got behind in the count."
Cole gave up three runs on three hits over 2 1/3 innings in his professional debut Oct. 14. In that start, he faced 11 batters and threw 35 of 52 pitches for strikes.
Originally selected in the first round by the Yankees in 2008, Cole did not sign and instead chose to attend UCLA, which he called "the best decision of my life." After becoming the first player in school history to strike out 100 in each of his first three seasons, the Pirates made him the top overall pick in June.
Though that lofty Draft status comes with expectations, Cole said it does not bother him.
"Fortunately, I've lived with a little pressure ever since high school," he said.
In the AFL, he's keeping his goals simple.
"Just getting a consistent delivery," Cole said. "Getting comfortable, being in control and making pitches."