[WATCH: All Stars vs. Blues highlights]
Allen's first shutout of the season, a 3-0 win against the Dallas Stars at Scottrade Center on Thursday, was his 16th in the NHL, which tied the Hockey Hall of Famer for third in Blues history.
"It's pretty cool," said Allen, who made 29 saves. "I think it was a lot harder for Glenn to make shutouts back in the day than it is for us. I'll take it, and it's pretty cool to have that under my belt, and hopefully I get a lot more in the next few years."
Brayden Schenn, Colton Parayko and Vladimir Tarasenko scored for St. Louis (19-8-2), which has won two straight.
Allen's shutout was his third in 11 games against the Stars.
"Jake, I thought, was really good tonight," Blues coach Mike Yeo said. "He was sharp, engaged and focused right from the start."
Video: DAL@STL: Allen sprawls to deny Stars late in 3rd
Kari Lehtonen made 24 saves for the Stars (16-12-1), who have lost two in a row after a five-game winning streak. They were shorthanded seven times and allowed two power-play goals.
"I think it's more why we took the penalties," Dallas coach Ken Hitchcock said. "We took the penalties because we were second place to the puck. They won the race and we took the penalty because of it. We got beat, got beat to a lot of the races on the penalties we took, poor stick positioning, poor sticks. Any momentum we started to build, we got it taken away with penalties."
Schenn's 14th goal of the season gave the Blues a 1-0 lead at 13:39 of the first period off a rebound to the right of Lehtonen. Schenn had a hat trick in a 4-3 win against the Montreal Canadiens on Tuesday.
"That's just a great play by [Alexander Steen], where he was able to get a puck through, and I think [it was] me and [Dmitrij Jaskin] 2-on-1 pretty much in front of the net," Schenn said.
The Blues had four power plays in the first period, including a 5-on-3 for 1:14, but did not score.
Stars defenseman Stephen Johns almost tied the game in the final second of the second period. His shot hit Allen and popped over the goalie into the net, but video review confirmed the puck went in after the period ended.
"The horn's always delayed in every arena," Allen said. "It's usually a second delayed, so you always know once the horn (sounds) ... the puck's in the net is probably the same time as the horn, so you always know it's late."
Parayko scored on a one-timer from the blue line at 5:01 of the third period, the Blues' second power-play goal, for a 2-0 lead. Paul Stastny set a screen in front of Lehtonen.
"They kind of went out to [Patrik Berglund] on the wall, and they were already on [Tarasenko] on the other side," Parayko said. "So it kind of seemed like I was alone in the middle. Great net-front by our team."
Tarasenko scored an empty-net goal with 48 seconds remaining, his first goal in seven games, 13th of the season.
Video: DAL@STL: Allen stones Ritchie with pad save
Goal of the game
Schenn's goal at 13:39 of the first period.
Video: DAL@STL: Schenn buries rebound for power-play goal
Save of the game
Allen's save on Jamie Benn at 19:58 of the second period.
Video: DAL@STL: Allen sprawls to rob Benn before period ends
Highlight of the game
Parayko's goal at 5:01 of the third period.
Video: DAL@STL: Parayko blasts power-play goal past Lehtonen
They said it
"I don't think we played a good game, and we took too many penalties, and you can't do that if you want to win hockey games. You have to score goals. That's the bottom line, and we weren't able to do that today, so that's the No. 1 thing, obviously. Everybody has to just look in the mirror, all of us, regroup, and it's enough talking. I think we just have to show up and play." -- Stars forward Alexander Radulov
"We knew special teams were going to be important tonight and, first and foremost, I think that with the penalty kill, we did a good job, being disciplined, staying out of the box, and obviously we killed them when we need to, but all in all, big win." -- Blues coach Mike Yeo
Need to know
The Blues recalled goaltender Ville Husso from San Antonio of the American Hockey League to back up Allen after Carter Hutton sustained a lower-body injury during the morning skate. Amateur goalie Tyler Stewart was Allen's backup until Husso arrived with 5:09 remaining in the first period. … The Stars are 0-6-0 against the top three teams in the Central Division (St. Louis, Nashville Predators, Winnipeg Jets) and have been outscored 25-8. … Brian Elliott had 25 shutouts for the Blues, and Jaroslav Halak had 20. … Stars left wing Antoine Roussel (illness) missed his fourth straight game.
Stars: Host the Vegas Golden Knights on Saturday (8 p.m. ET; FS-SW, ATTSN-RM, NHL.TV)
Blues: At the Detroit Red Wings on Saturday (1 p.m. ET; SN1, FS-D, FS-MW, NHL.TV)
Video: Allen, Blues shut out Stars, 3-0