Patrick Kane and Michael Rasmussen each had a goal and an assist for Detroit (31-20-6), which has won four straight games. Alex Lyon made 22 saves.
The Red Wings, who have not qualified for the Stanley Cup Playoffs in the past seven seasons, currently hold the first wild card in the Eastern Conference.
"We're in a stretch where we are playing some really good hockey, and we need to take advantage of it," Red Wings coach Derek Lalonde said. "If we want to get over that (playoff) line at the end of the season, we're going to need every last point we can get."
Zachary Bolduc scored his first NHL goal for the Blues (30-25-2), who have lost three of four. Jordan Binnington allowed four goals on 14 shots in the first period and was replaced by Joel Hofer (18 saves) at the start of the second period.
"I think we had 22 or 24 turnovers in the first period -- that's normally how many we have in a game," Blues interim coach Drew Bannister said. "'Binner' was under siege out there -- this had nothing to do with him. He didn't have a chance."
Kane made it 1-0 33 seconds into the first period, one-timing a pass from Shayne Gostisbehere.