Datsyuk was the first shooter and he slipped a backhander past Cristobal Huet for the lead.
Valtteri Filppula and Jiri Hudler each had a goal and an assist while Conklin finished the game with 28 saves for the Red Wings, who have won their last three games.
Toews scored twice and Andrew Ladd had a goal and an assist for the Blackhawks, who have dropped four of their last five games. Huet made 26 saves in the loss.
Trailing by a pair of goals to start the third period, Detroit scored twice less than four minutes apart to tie the game.
On the power play, Johan Franzen skated the puck into the Chicago end and from the left boards flicked the puck to the slot where Henrik Zetterberg chipped it past Huet at the 6:32 mark.
Marian Hossa then tied the game as he flicked a shot into the left corner of the net from a sharp angle at the right side with 9:37 to play in regulation.
After Detroit scored two goals less than five minutes into the game, Chicago scored four straight to take the lead.
On the power play, Sharp and Kane worked a give-and-go with Kane sending the puck back to Sharp at the low left circle for a one-timer past Conklin at the 9:08 mark of the first.
Toews tied the game on a beautiful individual effort as he skated down the left wing, turned a defender inside-out and slipped a backhander past Conklin with 3:33 left in the first.
Chicago then took a lead into the first intermission as Toews fired a wrister from the low right circle that beat Conklin over the left shoulder with just 4.3 seconds left on the clock.
In the second, Chicago took a 4-2 lead just two minutes in as Dave Bolland fired a turnaround pass from the low left circle to the slot where Ladd one- timed the puck into the net.
Huet stopped seven shots in the second period to preserve Chicago's lead.
Detroit scored just 1:32 into the game as Filppula's one-timer from the left circle got through a screen and past Huet.
Just three minutes later, Huet attempted to play the puck behind his net, but Filppula wound up with the puck and sent it to Hudler, who fired the puck into the empty net from the left circle for a 2-0 lead.