After the first two rounds of the tiebreaker didn't produce a goal, Lapierre came in slowly on Detroit's Jimmy Howard and, after a pair of fakes, lifted a backhanded shot into the upper corner of the net.
Cory Schneider then closed out the win with a stop on Damien Brunner, securing a post-season berth for the Northwest Division-leading Canucks.
Schneider finished with 33 saves -- including 17 in the third period -- and Alexander Edler scored in regulation for Vancouver, which snapped a two-game skid.
Cory Emmerton scored and Howard made just 13 saves for the Red Wings, whose playoff hopes took a blow with the setback.
Detroit ended the night one point behind Columbus for the eighth and final Western Conference post-season slot with four games remaining.