Detroit advanced for the second successive season to the Campbell Conference final series against the Edmonton Oilers. That best-of-seven series begins Tuesday night in Edmonton. The Oilers beat the Red Wings in five games last year.
Higgins took a loose puck along the right boards, skated around defenseman Paul Cavallini, and beat St. Louis goalie Greg Millen with a backhand shot for the unassisted goal.
Millen made more than twice as many saves as Detroit goalie Greg Stefan, stopping 27 to 13 for Stefan.
Steve Bozek's first playoff goal gave St. Louis a 3-2 lead at 4:04 of the third period. Bozek snapped a wrist hot from the slot over Stefan's glove.
But John Chabot's third goal 1:37 later tied it. Chabot took a pass from Bob Probert and beat Millen from the left face-off circle.
Detroit led, 1-0, in the second period when Chabot threw a blind pass around the boards. Paul Cavallini kept the puck in the Detroit zone and shot from inside the blue line. Herb Raglan tipped it past Stefan's glove at 1:29 to tie it 1-1. It was Raglan's first playoff goal.
Bernie Federko gave St. Louis a 2-1 lead with his second playoff goal on a power play at 7:02.
Probert's fifth goal, also on a power play, tied it 2-2 at 11:18 of the second period.
Detroit's Lee Norwood scored his second playoff goal at 17:22 of the first period while the Blues' Tony McKegney was in the penalty box.