Lucas Raymond sent a pass into the offensive zone, and Larkin beat Shane Pinto to the puck before sliding a backhander between the pads of Linus Ullmark.
Raymond had two assists, and John Gibson made 26 saves for the Red Wings (34-19-6), who had lost four of five (1-3-1).
Brady Tkachuk scored, and Linus Ullmark made 18 saves for the Senators (28-22-8), who are 5-1-1 in their past seven games.
It was the first game for each team following the break for the Olympics.
Michael Rasmussen appeared to give the Red Wings a 1-0 lead at 8:11 of the first period, but Ottawa challenged the play for offside, and the call was reversed after a review.
Tkachuk put the Senators up 1-0 at 18:44 with a wrist shot from the high slot while on the power play. Jake Sanderson's shot from the point deflected off Rasmussen to Tkachuk, who beat Gibson through traffic. Tim Stutzle's secondary assist on the goal extended his point streak to eight games (six goals, five assists).
Larkin tied it 1-1 with a power-play goal at 5:24 of the second period, finishing Raymond's backhand pass from the goal line with a snap shot from low in the left circle to the glove side on Ullmark.
