Red Wings winger Johan Franzen erased a 2-0 deficit by scoring twice late in the third. Then, after a scoreless overtime, Todd Bertuzzi buried the only goal of the shootout on the final attempt to give the Red Wings the win.
"We haven't had a shootout against (Blues goalie Brian Elliott) and I was just trying to get an idea what he's like," Bertuzzi said. The veteran now has 10 career game-deciding goals in shootouts.
"Watching (Pavel Datsyuk) and (Jiri Hudler) shoot, I was trying to get a move in laterally and trying to get up as high as I can."
Detroit (48-27-5) are now fourth in the Western Conference, one point ahead of Nashville, while the second-placed Blues (48-21-11) trail leaders Vancouver by two points.
Both the Red Wings and Blues have two games remaining.
The two teams battled through two periods of scoreless action before St. Louis seized the advantage in the third with goals from David Perron and Andy McDonald.
Jimmy Howard finished with 27 saves in the win while Elliott had 26.
In the league's only other game, Montreal defeated Tampa Bay 5-2 and prevented league-leading scorer Steven Stamkos from adding to his goal total.
"I think everyone was well aware of how they were trying to feed him," Canadiens coach Randy Cunneyworth said. "I think we paid pretty good attention to him."
Stamkos has 58 on the season and has two games remaining to potentially reach 60, a milestone last reached in the 2007-08 season by Alex Ovechkin of the Washington Capitals.