Allen is now tied for third in franchise history, trailing only Brian Elliott (25) and Jaroslav Halak (20) on the Blues' all-time list.
"It's pretty cool," Allen said of tying Hall. "I think it was a lot harder for Glenn to get shutouts back in the day than it is for us now. But I'll take it. It's pretty cool to have that under my belt and hopefully I'll get a lot more in a few years."
Entering Thursday's game, Allen was 14-6-2 with a 2.75 goals-against average and a .906 save-percentage.
BLUES SHUTOUT LEADERS
1. Brian Elliott - 25
2. Jaroslav Halak - 20
3. Jake Allen - 16
Glenn Hall - 16
5. Roman Turek - 13
6. Brent Johnson - 12
7. Grant Fuhr - 11
8. Manny Legace - 10
Jacques Plante - 10
Mike Liut - 10