The home side drew on the first day of the new season but have since crashed to four defeats in a row.
Striker Andy Gray made a dream home debut when he fired Barnsley into an 11th-minute lead with the club's first goal at Oakwell this term.
Gray was pursued by Barnsley manager Simon Davey throughout the summer until he finally landed the 31-year-old just over a week ago for a reported £500,000 fee from Charlton Athletic.
Gray was on hand to power in an accurate header from a corner to confirm the home side's early domination.
Barnsley had more chances when Hugo Colace saw a shot blocked and Jamal Campbell-Ryce fired wide.
Gray almost grabbed a bizarre second when keeper Adam Federici's clearance ricocheted off him and ran just wide of the open goal.
As Reading fought back, Gylfi Sigurdsson hit a spectacular 25-yard free-kick that brought a super save from Luke Steele.
And four minutes later Reading earned a deserved equaliser although they were helped by a mistake from Colace.
Jimmy Kebe cashed in, and when Steele saved his fierce low shot, Alex Pearce snapped up the rebound and slammed in a shot from 12 yards out.
Reading began to dominate after levelling and should have taken the lead after 37 minutes but Jem Karacan turned a shot wide with only Steele to beat after the visitors broke away.
Two goals in three minutes from Hunt put Reading firmly in the driving seat early in the second half.
The first came after the visitors were handed a penalty when Kebe crashed down in the area when Steele dived at his feet. Hunt crashed in an emphatic spot-kick.
Three minutes after that a super cross from Kebe had the home side in trouble and Hunt guided a smart header out of Steele's reach.
Reading should have added another but when Pearce was handed a free header it flew over the top.