Akos Buzsaky scored twice to add to Mikele Leigertwood's opener as Rangers roared into a three-goal lead at half-time.
Barnsley hit back twice at the start of the second half, but Ben Watson and Jay Simpson ensured the points stayed in west London with Rangers starting to look like a team capable of staying with the promotion pace.
Controversial co-owner Briatore was not in attendance, despite having an unexpected free weekend following his F1 ban.
But his mood would have improved with news of a fine display from Rangers which halted Barnsley's resurgence under Mark Robins.
The new Tykes boss handed full debuts to three of his back four - and it showed with the visitors two down in 15 minutes.
Yet Barnsley twice went close in the opening stages with Anderson de Silva firing over and Iain Hume shooting wide.
Rangers went ahead in the sixth minute when Leigertwood loped forward from right-back and, with no Barnsley defender showing any inclination to close him down, fizzed a low shot past David Preece from 25 yards.
And the hosts were two ahead when Watson slipped Buzsaky in behind and the Hungary international tucked the ball past Preece.
It could have been three two minutes later but Wayne Routledge's angled drive fizzed across the goal and flicked the far post.
But Buzsaky did add the third five minutes before half-time when he collected the ball 30 yards out, looked up and curled a superb effort over Preece and into the net.
It was a sweet moment for the 'Magical Magyar', scoring his first goals of the season having missed most of last term through injury.
Rangers never like to make life too easy for themselves, though, and Barnsley pulled one back at the start of the second half when Stephen Foster rose highest to nod Iain Hume's cross past Radek Cerny.
And five minutes later the deficit was back to one when Damion Stewart tripped Adam Hammill in the area.
Andy Gray's spot-kick was saved by Cerny but the ball fell kindly for the striker to tuck away the rebound.
Cerny tipped Hammill's long-range effort over the top to preserve Rangers' lead in the 63rd minute.
Three minutes later Buzsaky's cross was headed back across goal by Rowan Vine and Watson's effort was fumbled over the line by Preece. And Rangers were home and dry when Kaspars Gorkss's header caused more mild panic in the Barnsley box and Simpson got the final touch to complete the scoring.