Mrazek's first game at pro hockey's highest level came at the age of 20 and he reacted like a veteran while his teammates gave him plenty of support. Detroit had been outscored 28-23 in its first nine games.
Daniel Cleary and Jakub Kindl gave the Red Wings a 2-0 lead with their first-period goals.
Alex Pietrangelo delivered the only score for St. Louis with 4:15 to go in the second period, but before that stanza was over the Red Wings had produce two more goals to take control.
Cory Emmerton scored with 2:27 left in the period and Damien Brunner came through with 56 seconds left. Valtteri Filppula finished the scoring with his third-period goal.
Brian Elliott was charged with all five goals on 29 shots.
Aaron Carter is still in love with Hilary Duff
NBC reportedly holds celebs hostage to Jimmy Fallon's show