Keane's Ipswich side were poor in midweek as they suffered a home defeat at the hands of Derby and they were again picked off with ease by a visiting side as Mark Robins led his side to three valuable points.
Winger Goran Lovre opened the scoring before a Marton Fulop own goal doubled the lead before the break.
Garry O'Connor wrapped up the win with a simple finish to leave the home fans far from happy with Keane.
The former Manchester United captain was the subject of derisory chants all afternoon from the home crowd, who ended the game ironically cheering every Barnsley pass.
They were given a crumb of comfort when defender Tommy Smith headed in late on but the Tractor Boys were well beaten on the day.
The home side were without several players and Grant Leadbitter's suspension saw on-loan Jack Colback moved into the centre of midfield.
The youngster made his mark instantly with a cynical challenge on Lovre which saw him booked inside three minutes.
The Tykes then launched a rapid counter attack and played dangerman Adam Hammill into space, but Mark Kennedy recovered sharply to make a fine tackle.
Barnsley were controlling large spells of possession but the home side came close to opening the scoring when Tamas Priskin fired in a shot from the edge of the area but Barnsley goalkeeper Luke Steele tipped the ball on to the bar.
It was unlucky for the hosts but they could have few complaints when Lovre put the Tykes ahead in the 21st minute.
The influential Hammill carried the ball forward and dug out a deep cross to the far post.
Jim O'Brien timed his run well to head the ball back across the face of goal to leave Lovre with the simple task of volleying into the net from six yards.
The Portman Road crowd were growing restless and were incensed moments later when O'Connor waltzed through a statuesque backline and should have doubled the lead but dragged his shot wide.
However Hammill soon found his range again as it was 2-0 in the 27th minute.
He unleashed a powerful shot from 25 yards which struck the foot of the post and cannoned into Fulop's back before nestling in the back of the net.
It was unfortunate for the Hungarian goalkeeper and his compatriot Priskin was also unlucky before the break when his shot flew wide.
Keane was being urged to "sort it out" by the home support and he made two changes at the break, introducing youngsters Luke Hyam and Ronan Murray in a bid to win back the battle in midfield.
But any hope of a comeback was extinguished within five minutes of the restart when O'Connor made it 3-0.
Lovre took advantage of some slack marking to break clear on the left wing before supplying a low ball into the goalmouth which the on-loan Birmingham man steered inside the near post.
Barnsley were again passing the ball with ease and the home crowd lightened the mood by cheering each successful ball.
Smith at least ensured some good news for Keane when he responded in the 80th minute with a powerful header from a Carlos Edwards corner.