The visitors adapted far better to the wet conditions and David McGoldrick raced clear in the fifth minute only to fire high and wide.
With the next attack, Paul Anderson went down in the area but the referee waved play on.
Anderson was causing the Bluebirds defence all sorts of trouble and he flashed one shot inches beyond the far post as Forest continued to have the upper hand.
In the 21st minute, in a rare City attack, Peter Whittingham struck a volley that was tipped over the bar at full stretch by Forest keeper Lee Camp.
Midway through the half, Stephen McPhail left the field injured and his place was taken by Gavin Rae.
The Blubirds began the second half looking more like a side shooting for top place in the division and, in the 56th minute, only a goal-line clearance stopped them from taking the lead.
Dele Adebola joined the fray in the 62nd minute, but it was the Bluebirds who opened the scoring just 60 seconds later. Joe Ledley threaded a pass through for Bothroyd who fired across Camp and into the far corner for his fifth goal of the season.
Forest were stunned by the goal and used all three substitutes to try and get back in a game they had controlled for long periods.
In time added on a mistake at the back let in sub McGugan and he blasted his shot beyond David Marshall for a deserved equaliser.
There was still time for Michael Chopra to receive a yellow card before the referee blew the final whistle.