Braney scored the equaliser from a tight angle against Dorchester Town as the Generals went on to win 3-1 - their fourth win in succession.
Aribim Pepple returned to action for the first time since the end of October, coming on as a second half substitute in Grimsby's 1-0 defeat against AFC Wimbledon.
John McAtee started the game and had the ball in the back of the net in the 13th minute after rounding goalkeeper Nik Tzanev, but the forward was adjudged to be in an offside position when he received the ball.
After Wimbledon had taken the lead through Ethan Chislett, Pepple was brought on to partner McAtee but Grimsby were unable to find a reply.
Elsewhere in League Two, Josh Neufville played the full 90 minutes as he helped Sutton United claim a point on the road against Carlisle United. The home side took the lead on the half-hour mark, before Will Randall replied just before half-time.