The 38-year-old keeper foiled Marcus Tudgay three times in quick succession as the Sheffield side bombarded QPR who had beaten city rivals Sheffield United just two weeks earlier.
Wednesday, reinforced by new loan signings Scott Carson and Mikkel Bischoff, started in dramatic fashion.
Burton O'Brien, in space on the left, pumped over a precise cross picking out Deon Burton whose stinging header at the far post was palmed around the woodwork in spectacular fashion by Jones.
The Hillsborough side went ahead in the 13th minute as Burton snatched his first for the club since his £120,000 moved from neighbours Rotherham in January.
Glenn Whelan pumped the ball into the area and the 30-year-old striker stuck out a foot to divert it past Jones from 12 yards.
Peter Gilbert foiled Paul Furlong before Rangers were back on level terms three minutes ahead of half-time after Whelan gave away a needless free-kick.
Lee Cook curled in a low cross and Marc Bircham steamed in to finish with a stooping header from close range.
Jones pulled off a string of saves in a frantic few seconds as he kept out Tudgay three times before Yoann Folly hit the bar from 10 yards.
Tudgay had a header hacked away by Mauro Milanese as the Sheffield side bombarded the Rangers goal.
Carson pulled off an eye-catching stop on 68 minutes as he pushed Cook's curling free-kick around the post.