Daley's seventh goal of the season was the only shot on net during the overtime session. Andreas Athanasiou and Darren Helm had the regulation goals for the Red Wings, who won for the second time in as many nights.
Detroit goalie Jimmy Howard turned aside 36 shots.
J.T. Miller and Jesper Fast scored for the Rangers, who have lost seven straight for the first time since 2006. New York goaltender Henrik Lundqvist made 31 saves.
The Rangers were playing their first game since trading away All-Star winger Rick Nash. New York acquired a first-round pick in this year's draft, defenseman Ryan Lindgren and forwards Ryan Spooner and Matt Beleskey and a seventh-round pick in next year's draft in the deal with the Boston Bruins.
Spooner assisted on both goals in his Rangers debut.
Athanasiou scored the only goal of the first period when he skated in along the right side and beat Lundqvist through the five hole at 19:53.
Helm's unassisted goal at 4:31 of the second period made it 2-0. Following a Rangers giveaway in the Detroit zone, Helm skated in on a breakaway and fired in his eighth goal of the season.
Miller ripped a shot from the left circle past Howard on a power play at 7:51 of the second period. Red Wings forward David Booth was in the penalty box because of a tripping infraction.
Tomas Tatar appeared to give Detroit a 3-1 lead moments later when his rebound shot trickled past Lundqvist. However, the Rangers challenged, and the officials ruled that the Red Wings were offside when they entered the zone.
New York knotted the game on Fast's goal at 11:16 of the third. Fast banged home a rebound after Howard robbed Kevin Hayes.
The Red Wings clinched the season series 2-1. The Rangers won the first meeting 2-1 in overtime on Nov. 24, and Detroit won a shootout 3-2 on Dec. 29.
--Field Level Media
Detroit | NY Rangers | |
Andreas Athanasiou 1 | Points | Ryan Spooner 2 |
Andreas Athanasiou 1 | Goals | Jesper Fast 1 |
Nick Jensen 1 | Assists | Ryan Spooner 2 |
N/A | Power Play Goals | J.T. Miller 1 |
N/A | Short Handed Goals | N/A |
Jimmy Howard .947 | Save Percentage | Henrik Lundqvist .912 |
Jimmy Howard 36 | Saves | Henrik Lundqvist 31 |
Team | Shots | Goals | Power Play | Penalty Kill | Penalty Mins | Face Offs Won |
Detroit | 34 | 3 | 0-3 | 1-2 | 4 | 32 |
NY Rangers | 38 | 2 | 1-2 | 3-3 | 6 | 36 |