Lewin Nyatanga and Conor Hourihane had given the Tykes the lead before Jones hit back just before the half time whistle.
Nyatanga grabbed his second of the game in the second half to seal the victory for Barnsley.
Latics started the game brightly with the supporters right behind Dean Holden's men.
With Latics doing much of the early pressing, Latics were caught on the break and captain Adam Lockwood received a booking for bringing down John O'Sullivan down as he raced through on goal.
New loan signing Luke Woodland looked promising in midfield and played Jonathan Forte down the left on ten minutes. Forte's cross was a good one into the box but just too far for Jones to latch onto.
Barnsley started to grow into the game and could have taken the lead on 13 minutes. Martin Cranie rose highest from Ben Pearson's corner but he headed over Jake Kean's crossbar.
Although both sides enjoyed good spells of possession, neither side really threatened in front of goal with 30 minutes on the clock.
However, the game exploded into life just after the half hour mark as Barnsley took the lead.
Hourihane's free kick into the box was parried by Kean into the path of Nyatanga who finished from close range to give the visitors the lead.
The Tykes had a great opportunity to make it two just two minutes later.
Connor Brown received a booking for a handball on the edge of the box and Hourihane stepped up to fire just wide of the post from 25 yards.
Barnsley extended their lead in fortuitous circumstances on 39 minutes.
Carl Winchester attempted to smash the ball away from danger but his clearance was blocked by Hourihane and it ended up in the back of Kean's goal to make it two.
Latics needed a response and got it as they reduced the arrears three minutes before the break.
Conor Wilkinson guided the ball into the path of the onrushing Jones and he finished confidently into the corner to give Latics hope for the second half.
Just before the half time whistle, Woodland was booked for a high challenge on Josh Scowen.
Latics began the second half showing attacking intent and the fans responded by creating an intimidating atmosphere.
Five minutes into the half, Mat Sadler, on his home debut, crossed into the box and Barnsley goalkeeper Adam Davies fumbled but Latics could not get the ball over the line.
All the pressure was coming from Latics and Wilkinson struck goalwards just before the hour mark but Davies saved well.
Barnsley made their first change to the afternoon and brought Sam Winnall on to replace Lalkovic but Latics were still in the ascendancy.
Wilkinson had Athletic's best chance on 66 minutes. The striker received the ball inside the area, turned his defender but Nyatanga was there just to deflect the ball past the goal and out for a corner.
From that resulting set piece, Sadler stabbed the ball just wide of the post from 25 yards.
Barnsley managed to regain their two goal advantage with 20 minutes of the game remaining.
After a scramble in the box, Nyatanga managed to scramble home his second of the game to put Lee Johnson's men 3-1 ahead.
Latics needed another response but were met by a stubborn Barnsley defence as they lost the impetus from the start of the half.
Into the last ten minutes of the game, Latics had two chances to get a goal back.
First, substitute Rhys Murphy had a sight of goal but could not connect properly with the ball when presented with the chance and Wilkinson forced the goalkeeper into a good save at his near post.
Latics were still knocking on the door and Forte was the next to see his shot saved by Davies. From the resulting corner, the goalkeeper pulled off a wonderful save to deny Wilkinson from pulling a goal back.
Deep into additional time, Lockwood received his second booking of the game and will miss Tuesday's fixture with MK Dons.
Oldham Athletic: Kean, Brown, Lockwood, Kusunga, Sadler, Woodland, Winchester (Turner 87'), Jones, Philliskirk (Murphy 71'), Forte, Wilkinson.
Subs not used: Coleman, Dieng, Mellor, Bove, Jacobs.
Barnsley: Davies, Holgate, Cranie, Nyatanga, John, O'Sullivan, Lalkovic (Winnall 61'), Pearson (Bailey 81'), Scowen, Hourihane, Waring (Ibehre 87').
Subs not used: Dibble, Smith, M'Voto, Jennings.
Goals: Oldham Athletic (Jones 42') 1-3 Barnsley (Nyatanga 33', 70', Hourihane 39')
Attendance: 6,344 (2,471 visiting supporters)