Erik Johnson and Andy McDonald also scored for the Blues, and Paul Kariya had three assists. Manny Legace made 36 saves.
Johan Franzen scored twice and Brian Rafalski netted Detroit's other goal. Henrik Zetterberg and Pavel Datsyuk each had three assists, and Chris Osgood stopped 17 shots.
Boyes put in a one-timed shot from the left circle 2:43 into overtime.
Franzen tied it at 3 with 4:41 left in regulation when he tipped in Zetterberg's pass from the right boards for his 25th goal.
Franzen's first cut Detroit's deficit to 3-2 with 6:33 remaining in the third when he put in a rebound for a power-play goal.
Johnson gave St. Louis a 2-0 lead with a power-play goal 4:29 into the second period. His one-timed slap shot from the left point deflected in off Franzen's skate.
The Red Wings got on the board with a power-play goal just 38 seconds later.
Just 11 seconds into Jay McClement's hooking penalty, Rafalski scored his 13th goal.
McDonald gave St. Louis a two-goal lead 9:28 into the third period when he beat Osgood with a wrist shot from the right circle for his 17th goal. McDonald picked up the puck just outside Detroit's blue line after a turnover by Jiri Hudler.
The game featured the return of Darren McCarty, who made his season debut with the Red Wings. The forward had been nursing injured ribs after being recalled from a conditioning stint with Grand Rapids of the AHL on March 7. He played with the Red Wings from 1993-2004 and hadn't been in the NHL since last season with the Calgary Flames.
Boyes opened the scoring with 7:40 left in the first period when he converted Kariya's backhanded pass from behind the net for his 39th goal.
Notes:@ Detroit was without D Brad Stuart (broken finger), RW Mikael Samuelsson (groin), RW Tomas Holmstrom (lower abdominal) and G Dominik Hasek (flu). ... St. Louis D Jay McKee returned after missing three games with a foot injury. ... Detroit LW Dallas Drake was honored before the game for playing 1,000 NHL games. ... Three of Johnson's five goals were scored against the Red Wings. ... Franzen has 13 goals and four assists in 12 games.