The main action of the Championship clash came in the final 20 minutes as Eric Lichaj gave Nottingham Forest the lead only for the Reds to lose their captain Henri Lansbury shortly afterwards.
He was red-carded for a poor tackle to signal a concerted spell of pressure from Burnley which culminated in Taylor's goal.
Dougie Freedman's side hung on for a point in front of 17,721 and will now prepare for the visit of Ipswich Town this weekend.