Benn finished off a cross-ice pass from Miro Heiskanen, beating a sprawling Jordan Binnington from the right face-off dot to put the Stars up 5-4 after they had blown a two-goal, third-period lead.
Benn also had an assist, Jason Robertson and Matt Duchene each had a goal and an assist and Jake Oettinger made 14 saves for the Stars (34-14-9), who enter the Olympic break having won six straight and seven of the past eight games.
Jordan Kyrou and Jimmy Snuggerud each had a goal and an assist, and Justin Faulk had two assists for the Blues (20-28-9), who enter the Olympic break with only one win in the past nine games (1-7-1). Binnington made 23 saves.
Snuggerud cut the lead to 4-3 at 10:05 in the third period on a shot from the high slot through traffic.
Alexey Toropchenko tied it 4-4 at 15:31 when he rushed the front of the net and Philip Broberg spotted him with a no-look backhand pass from below the goal line.
Pavel Buchnevich gave the Blues a 1-0 lead at 7:29 of the first period on a one-timer from the left face-off circle on the power play.
Robertson tied it 1-1 at 11:37 on a wrist shot at a sharp angle from the goal line when Mikko Rantanen found him on a cross-ice pass. It was his 200th NHL goal.
Kyrou gave the Blues a 2-1 lead at 18:33 on a shot from the right face-off circle that picked the far corner over Oettinger’s shoulder.
Duchene tied it 2-2 at 1:56 in the second period on a rebound shot from the bottom of the right circle on the power play.
Mavrik Bourque gave the Stars a 3-2 lead at 3:58 when he capitalized on a rebound in the slot.
Benn extended the lead to 4-2 at 11:57 on a wrist shot from the inside of the left face-off circle.
