In 47 games during the regular season, Allen was 26-15-3 with a 2.35 GAA and .920 save percentage. He had a 2.20 goals-against average and .904 save percentage starting all six games of a first-round loss to the Minnesota Wild in the 2015 playoffs.
Elliott, who has started all 17 games for St. Louis this postseason, is 9-8 with a 2.34 GAA and .925 save percentage. He was 23-8-6 with a 2.07 GAA and .930 save percentage in 42 regular-season games.
Neither Allen nor Elliott was available for comment Friday.
"I think, quite frankly, we've had two guys all year," Hitchcock said. "It might be a story for people, but for inside the locker room and for us as coaches, it is kind of an easy decision in the fact that, you know, it's probably easier for us than it is for other people because we've just trusted both guys so much.
"We trust Brian. Even when there were bumps, we trusted Brian. I think this is a little bit different. This is a change in momentum."
St. Louis has lost the past two games 4-0 and 3-0 after winning Game 1 2-1.
"You win championships with defense," Hitchcock said. "Both teams are committed to defense, but they [are] being a little bit better at it than us, quite frankly. That's why they have the 2 1 lead. ...
"We have to make a change. Everyone is on a short leash, forwards, [defensemen]. ... Everybody's on a short leash. Give us what you got, we'll see it from there."