The Clarets felt they were on the wrong end of several refereeing decisions, having a penalty shout turned down and a goal chalked off either side of the break, while Henderson appeared to be offside for his late effort.
Ben Mee equalised for the hosts with his first Burnley goal, heading in Junior Stanlislas's corner at the near post.
Burnley's frustration was calmed when Charlie Austin converted a powerful header in first-half stoppage time for his 11th goal of the season, and Stanlislas thought he had extended the Clarets' lead just past the hour mark.
The former West Ham winger traded passes with Paterson before shooting low past David Forde, but the provider was adjudged to be offside more than a minute after the ball crossed the line.
These decisions proved to be costly for Burnley as Henderson levelled the scores after 92 minutes by poking home from close range.
Remarkably, the visitors almost won it when Henderson's shot deflected off Mee and onto the crossbar, but Burnley survived to claim a more-than-deserved point.