Criss, 24, took over the role from "Harry Potter" actor Daniel Radcliffe, who originated the character for the revival last spring.
"Criss' shining moment was "I Believe In You," where Finch sings a pep talk into his washroom mirror as he makes his climb to the top. The staging puts Criss on a platform at the front of the orchestra, close to the audience. Although he's singing to himself, he manages to connect to the crowd and seems to tell them he believes in them, too," noted Billboard.com in its review.
Criss admitted he was very nervous before he hit the stage for the first time. "Everyone's like, 'Oh, I gotta go to your opening night!'" he told EW.com. "But I'm terrified. I'm like, 'No! See it at, like, two and a half weeks.'"
He will be performing on Broadway for a limited three-week run.
Criss's Broadway debut earned him a standing ovation.
Tony winner Lea Salonga congratulated Criss via Twitter. "Judging from the curtain call, I'd say the night went well. Congratulations, @DarrenCriss, and break a leg for the rest of your run!!!"
Salonga sang with Criss on the duet "A Whole New World" during a tribute to the song's composer Alan Menken.