City's fightback fell short at Oakwell despite scoring three goals in a dramatic second half.
Head coach Michael Skubala made four changes in the trip to the Tykes. Lewis Montsma, Ethan Hamilton, Tom Bayliss and Freddie Draper returned to the XI in place of Jovon Makama, Sam Clucas, James Collins and the suspended Paudie O'Connor.
City started on the front-foot with a Tom Bayliss cross from the left giving Draper the opening chance within the first five minutes. Unfortunately his header was just wide of the mark.
It was the hosts who took the lead on 14 minutes as a defensive mix up gave Davis Keillor-Dunn the opportunity to chip the ball over goalkeeper Zach Jeacock and into the net.
After some quick feet from Dom Jefferies his bending cross from the left was just too far in front of the on-rushing Ben House at the back post, with Michael Skubala's side looking for a quick response.
Jeacock denied the hosts doubling their lead on the half hour mark when Adam Phillips' effort from inside the box was held well by the Imps goalkeeper.
Phillips was not to be denied his goal as the Tykes gave themselves a two-goal cushion on 33 minutes. The midfielder was found on the right with time and space, and made no mistake with a low driven effort into the bottom corner.
City pushed for a way back into the game with Jefferies having an effort from inside the box on 42 minutes. He had to see his effort deflect wide for a throw in.
Two minutes later Draper had the best chance of the half, after a headed Bayliss pass found the striker. His powerful left-footed effort was wide at the front post.
The hosts added a third on 54 minutes as Georgie Gent picked up the ball on the left side of the box, before firing a shot into the roof of the net.
Skubala made a triple change following the goal seeing Hackett, Collins and Makama enter the game. Hackett almost made an immediate impact as a Makama cross was diverted goalwards by the winger, but the shot was blocked.
City pulled one back on 67 minutes as wing-back Tendayi Darikwa pounced inside the six yard box before smashing an effort past Jackson Smith.
City continued on the front foot and Hackett's driven shot from the edge of the box was parried away by Smith just a couple of moments later.
The Tykes restored their three-goal advantage with a quarter of an hour to play as substitute Max Watters won the ball in midfield before placing his short past Jeacock into the bottom corner.
Skubala's side kept pushing for a route back into the game and were rewarded when Reeco Hackett found the bottom corner with six minutes to play.
Barnsley goalkeeper Smith was called into action again as Makama was closed down in the penalty area, as the hosts looked to hang on.
City got a third goal as the hosts failed to clear a corner, leading to Jovon Makama poking the ball home in the second minute of stoppage time after some positive work from Joe Gardner.
City continued to push on but could not find a leveller late on.
Tykes: Smith, Russell, Roberts, O'Keefe (Lembikisa 46'), Phillips (Benson 58'), McCarthy, Gent (Barratt 82'), Earl, Keillor-Dunn (Rodrigues 81'), Humphreys (Watters 59'), Nwakali.
Unused subs: Flavell, Bland,
Imps: Jeacock, Darikwa (Hamer 80'), Montsma, Jackson, Roughan, Jefferies, Hamilton (Hackett 55'), McGrandles (Gardner 73'), Bayliss, House (Makama 55'), Draper (Collins 55').
Unused subs: Wickens, Clucas,
Attendance: 11,914 (1,217 away)
Referee: Scott Oldham
