Long struck in either half at the Madejski Stadium on Monday to take his tally to six goals in his last five games as Brian McDermott's side kept up the pressure on the play-off pack.
Caretaker manager Stuart Gray had seen Ross Wallace put Burnley briefly ahead but Long - who was superb throughout - soon levelled before finding a winner after the break.
The home side looked a threat from the off and striker Long came close to an opener inside the first five minutes.
Long was alert to rob Brian Easton of the ball and surge into the area. However the ball took an unkind bobble and he shanked his left-footed strike across the face of goal.
Long was looking his usual lively self and flashed a header wide after good work from Ian Harte before Jack Cork had Burnley's first effort with a dipping strike from 25 yards which flew over the top.
The visitors began to wrestle control of midfield with Cork and Chris Eagles influential, and the duo combined to create the opener in the 28th minute.
Eagles fed a fine overlapping run from Tyrone Mears and the full-back was able to cut the ball back perfectly for Wallace to strike home powerfully from 15 yards.
The goal shook up the home side and they were level within three minutes through the excellent Long.
Noel Hunt won a header on the halfway line and Long had the pace to race clear of the defence and the composure to slide the ball past goalkeeper Lee Grant.
Clarets midfielder Dean Marney then smashed a strike against the crossbar when a cross was not dealt with before the break as an end-to-end half came to a close.
Hunt almost put Reading ahead at the start of the second half when he narrowly missed Jimmy Kebe's cross from the right before Long fired wide.
The Royals were well on top as they continued their fine start to the second period and Long in particular was proving unstoppable.
First he drove to the byline and crossed for Kebe to fire wide and then he again got clear of the visiting defence but could not beat Grant.
But Long's persistence paid off when he headed home in the 68th minute.
Jobi McAnuff delivered the ball from the right and Long got across his marker to power in a header which gave Grant no chance.
Marney had the best chance to equalise for the Clarets when he arrived onto a deep cross but could only steer his volley wide.