The U's gave themselves a mountain to climb as a below par first half saw them two down at the break.
They came out brighter after half time - only to fall further behind - but gave it a real go in the final half an hour to seriously test the Tykes' mettle.
A flurry of chances late on could have got something for the U's, but they slip into the bottom four as a result of the defeat.
The game got off to a sluggish start as neither team really threatened the opposition’s goal during the opening phases.
Alfie Mawson had the best chance of the early exchanges as his header was saved by Jamie Jones following a Barnsley corner.
The Tykes took the lead after 18 minutes when Adam Hamill burst through on goal and after behind pushed wide by Jones, the ball fell into the path of Conor Hourihane who made no mistake and lashed the ball in from 6 yards.
Callum Harriott had a sniff of the Barnsley goal soon after with Eastman playing him in with a cross-field ball but his touch was slightly too heavy and Adam Davies raced off his line claim it.
The visitors extended their lead to two goals after Hamill found himself in space on the left hand side and coolly slotted past Jones from just inside the box.
The U’s best chance fell to Sordell whose fierce shot went narrowly wide from the edge of the box with Davies beaten just before half time.
The U’s started the second half in much better fashion than the first and had a host of chances in the opening 5 minutes.
Porter came on at half time and made an instant impact after his shot was pushed behind for a corner. Harriott whipped in the resulting corner and Eastman crashed a header against the bar.
Next, Richard Brindley found himself in space after being put through by Sordell and rifled a low shot inches wide past the post.
However, it was Barnsley who scored the first goal of the second half making it 0-3 as Marley Watkins led a counter attack and crossed from the by-line with Ivan Toney waiting to accurately head the ball into the far corner.
It appeared that the U’s were out of the game, but Chris Porter found George Moncur with a through ball after 67 minutes and he picked out the far corner excellently from 12 yards.
Porter made it a quick-fire double for the U’s after taking a Harriott cross on his chest and volleying superbly past Davies who only managed to get a fingertip to it on 69 minutes.
United had all the momentum and almost completed the comeback on 72 minutes as Harriott hit a volley from the edge of the box but Davies scrambled across his goal to keep it out.
Both Sordell and Moncur had chances in the final exchanges of the game and both went agonisingly close to levelling it. Sordell poked his shot wide from 8 yards and Moncur’s curling effort from 25 yards skimmed the post.
The U’s threw everything forward and brought Macauley Bonne on for Gavin Massey but were unable to find that equalizing goal.
A valiant fightback from The U’s in the second half probably deserved a point but they just left themselves with just too much to do.