Shane Long put the Royals ahead from the penalty spot after Leon Cort, who was later sent off, brought him down.
Jobi McAnuff's measured second-half effort, as well as goals from Michael Antonio and Simon Church ensured Reading claimed their first win away from home since a 2-1 victory at Leicester in August.
Reading forged ahead after six minutes when the isolated Long got the upper hand on Cort. The Clarets defender was clearly caught out for pace as Long wriggled his way goal-side.
Long took the kick himself and, although Brian Jensen guessed the right way, the ball found the bottom right-hand corner.
Burnley wasted a number of chances to get back into the game, but their task became harder in the 64th minute when McAnuff tucked home from the edge of the box.
Cort got his head to a Harte free-kick, but as it dropped on the edge of the box, McAnuff calmly side-footed beyond Jensen. Cort's second career red card then followed in the 67th minute after he clattered into Long.
Substitute Antonio then used his first touch to roll the ball in from point-blank range after Long's pull-back four minutes from time, and Church belted home a fourth deep into stoppage-time to seal the win.