With less than two minutes remaining in the extra period, Datsyuk gathered a rebound and lifted a wrist shot from a difficult angle into the net as the Red Wings rallied past their divisional rival, who were consigned to a fourth straight loss.
"It was a good screen and I hopped on the puck," Datsyuk said. "The goalie (Corey Crawford) just fell on the ice and I just shot and made sure I didn't miss."
Chicago led 2-0 on first period goals from Dave Bolland and Patrick Sharp but could not hold on to the lead and are now mired in their longest losing skid since they dropped five straight in 2009.
Detroit's Valtteri Filppula cut the deficit to 2-1 later in the first and that scoreline stood until Daniel Cleary tied the game with just under five minutes remaining in regulation.
Henrik Zetterberg assisted on both goals for the Red Wings.
With the win, Detroit (26-14-1) moved into a three-way tie at the top of the division with St Louis and Chicago.
"I see this battle going on all year and the conference is tightening up, as well. But we did give away a lot of ground here this week and it's up to us to regain where we're at," Chicago coach Joel Quenneville said.
The Blackhawks earned a one-goal win over the Red Wings in the United Center on Dec. 30 but have not won since.
Sharp, who recorded his 20th goal of the season, left the game in the second period with an upper-body injury and did not return. He will be evaluated on Monday.
Chicago also had a goal disallowed early in the third when it appeared a shot hit goaltender Ty Conklin and crossed the line but it was not ruled as a score and could not be reviewed.
Conklin finished with 29 saves and stopped a penalty shot from Jimmy Hayes in the third to keep his team in the contest.