This was a case of lightning striking twice as Jones also scored twice on his debut against QPR for his former club Crewe. To rub salt further into the wounds Rangers boss Gary Waddock tried unsuccessfully to sign Jones in the summer.
Rangers created the game's first chance with a free header for debutant Nick Ward but the Aussie midfielder placed his effort straight at Burnley keeper Brian Jensen.
Ward also showed his nose for goal with a strike from distance which Jensen did well to push away for a corner.
It took Burnley 30 minutes to create their first opportunity with Jones delivering a teasing cross to the far post where 18-year-old Kyle Lafferty headed over. Burnley's other 18-year-old, midfielder Chris McCann, tested Rangers keeper Paul Jones with a 20-yard strike just prior to the break.
Burnley took the lead with a messy goal as Jensen's long clearance eventually found Alan Mahon who in turn tried to find striker Andy Gray but although the pass was over-hit keeper Jones was slow off his line allowing the ball to break to striker Steve Jones who calmly fired home.
Not content with edging in front Burnley boss Cotterill signalled his positive intentions with a double substitution which saw Lafferty and James O'Connor replaced by Wade Elliott and Micah Hyde.
The change almost paid immediate dividends as Elliott caused panic in the defence before veteran Frank Sinclair blasted well over from 15 yards.
The home fans didn't have to wait long for a second as QPR left-back Mauro Milanese was caught in possession by Sinclair and Jones then found the top corner of the net with a stinging shot, an early contender for goal of the season.
Burnley's confidence grew with the hosts creating further chances for McCann, Mahon and Micah Hyde before the final whistle saved Rangers from a heavier defeat.