This twice-postponed match got off to the perfect start for the Rebels, with recent signing Barney closing down goalkeeper Ben Goode, blocking his clearance and slotting the ball in from a tight angle for his first goal in a Slough shirt.
Jhai Dhillon put a shot just wide of the post as Slough looked for a second, but Mark Scott was called upon to make a diving save from Bennett as he got on the end of a free kick.
Barney was twice almost teed up for a second goal, first seeing the ball cleared after Warren Harris' pass, and shortly after Scott Harris pulled the ball back for the striker with the goal gaping, but a poor touch allowed Goode to gather the ball.
Evandro Delgado threatened for Potters Bar, but he saw his shot saved by Scott as he burst clear, and from the resulting throw, Chris Doyle's shot was well gathered by the keeper.
On 38 minutes, the hosts equalised as Sean Grace found space in the middle of the penalty area to fire the ball past the outstretched arm of Scott.
Almost immediately though, Slough regained their lead with Barney again on target. Warren Harris was played in behind the Potters Bar defence and his cross was touched in by Barney for his second of the night.
The Rebels just about deserved their half-time lead, having put together good passages of play on a difficult pitch in windy conditions, but the hosts emerged a determined force in the second half, immediately putting Slough under pressure.
Slough were forced to clear the ball off the line early in the half with Potters Bar forcing the tempo, and Delgado fired another shot across goal and wide before having another deflected wide.
Scott came to the rescue to turn a long-range shot from Billy Adcock over the bar with Slough struggling to keep hold of the ball as they had done in the first half.
Clear chances were hard to come by for Slough, Scott Harris putting a shot wide, whilst the hosts continued to look dangerous. Sean Fraser was required to put in a crucial tackle to deny Jack Lyons as he looked to be running clear on goal.
Late in the game, Potters Bar got the equaliser their play had deserved as Ashley Nathaniel-George broke into the area and poked the ball past Scott to make it 2-2.
There was still time for Adcock to almost score a winning goal, but Scott dealt with his looping shot, tipping over the bar.
With 90 minutes up, the tie progressed straight to kicks from the penalty mark, but Slough got off to the worst possible start with Goode saving Hope's effort. Doyle scored for Potters Bar, but Goode saved again from Scott Harris leaving Dave Lawrence to make it 2-0.
Eddie Smith, a late substitute, scored Slough's only spot kick but Joe Bennett responded and when Charlie Mpi then had his effort saved well by the heroic Goode, the tie was over and Slough were left to focus solely on the league.
Potters Bar Town Line up
Ben Goode, Will Wambeek, Luke Warner-Eley, Gary Jones (c), Connor Sullivan, Sean Grace, Joe Bennett, Billy Adcock, Jack Lyons, Chris Doyle, Evandro Delgado. Subs: Dave Lawrence, Jerry Maja, Jordan Lawal, Ashley Nathaniel-George, Connor Samson.