Allen gets the start over All-Star Brian Elliott, who finished the season 26-14-3 with a 2.26 goals-against average and .917 save percentage.
"It's his turn," Hitchcock said of Allen. "He's been on this stage before, lots. He played in the playoffs in the American League [AHL], he's played world junior gold-medal games. He knows this stage. Nothing is going to shock or surprise him. The stage doesn't frighten him. That's No. 1."
Allen, 24, played in 37 games for the Blues this season, finishing 22-7-4 with a .913 save percentage and 2.28 goals-against average. He has one minute of NHL postseason experience, coming against the Kings in 2012.
His most recent AHL playoff experience came with the Chicago Wolves in 2014, and he finished with a .879 save percentage in nine games.
In 18 career NHL playoff games, Elliott is 6-10 with a .898 save percentage and 2.55 goals-against average.
"It'll be a good challenge," Allen said after practice Wednesday. "I've been working for this moment all year. To be able to get the start, it's going to be huge. I know we're all ready and excited to go."
Allen earned the opportunity with his strong play down the stretch for the Blues. With St. Louis fighting for position in a competitive Central Division, Allen came up big with a .961 save percentage in four April starts, winning three of them. In 16 games since the All-Star break, he posted a .930 save percentage, winning nine games.
"One guy has had a great season, and one guy has had a great last six weeks. We opted to go with the guy who has had a great six weeks," Hitchcock said. "[Allen] started to perform at a higher level. It looked like to me the game slowed down and looked like he was able to track pucks even quicker than at the start of the year, which was also a good sign."