Cash-rich Rangers began the campaign as one of the favourites for promotion, but their expectant fans were silenced when Iain Hume put Barnsley ahead after only five minutes.
Brian Howard's perfect pass put Hume through on goal and the £1.2million summer signing from Leicester capitalised by calmly slotting past goalkeeper Radek Cerny.
Rangers were struggling badly before hitting back with two goals from Hall in as many minutes.
First, Barnsley keeper Luke Steele parried Emmanuel Ledesma's free-kick into Hall's path and he bundled the ball home at the second attempt after his first effort came back off the bar.
Then, after Barnsley failed to clear a Lee Cook corner, the ball dropped to Hall near the edge of the area and the centre-back brilliantly hooked it back over his shoulder and into the far corner of the net.
Ledesma's through-ball gave Patrick Agyemang a chance to extend Rangers' lead early in the second half, but Steele blocked the striker's shot.
And Steele came to the visitors' rescue again when he dived to his right to save Hall's spot-kick, after Darren Moore had tripped Rangers forward Dexter Blackstock.
Steele also did well to keep out a Ledesma free-kick before seeing a driven shot from Rangers' Mikele Leigertwood flash just wide.
Barnsley never really looked like equalising and the best they could muster in the second half was a tamely-struck free-kick from Bobby Hassell, whose effort was easily saved by Cerny.
The Tykes played out the last six minutes with ten men after Van Homoet was red-carded for a crude challenge on QPR's on-loan Real Madrid midfielder Dani Parejo, who came on as a late substitute.