In the penultimate round of fixtures before the Olympic break, having let a two-goal lead slip for the third consecutive home game, the Blues made sure of the win when TJ Oshie scored three minutes and 29 seconds into extra time.
Tampa Bay are second to Boston and they were also beaten, losing 4-1 to the Toronto Maple Leafs.
Jonathan Bernier made 33 saves for the Maple Leafs who have now won 10 in 13.
Montreal sit third and they made it two wins in a row as they saw off the Vancouver Canucks 5-2, with Max Pacioretty scoring three goals, affording himself the luxury of two missed penalty shots.
Elsewhere in the East, Detroit made it six wins from their last 10 with a 3-1 win over the Florida Panthers, while the Buffalo Sabres were beaten 3-2 by Ottawa.
Washington remain alive in the race for the play-offs as they got the better of Winnipeg 4-2 thanks to three unanswered third-period goals.
Ben Scrivens enjoyed his night at Madison Square Garden as the Edmonton stopper made 35 saves from 36 shots as Edmonton won 2-1 against the New York Rangers.
Mark Streit, Michael Raffl and Claude Giroux all scored as the Philadelphia Flyers beat the Colorado Avalanche 3-1, while an overtime goal from Nino Niederreiter gave Minnesota a 3-2 win over Nashville.
The Los Angeles Kings were also overtime winners, beating Columbus 2-1, while the New York Islanders were beaten 3-1 by Calgary.