The Bees pulled off a dramatic comeback as they came from two-nil down to secure all three points in the final minute of the match.
The hosts took the lead inside the first five minutes as an Altrincham free-kick fell as far Ryan Colclough who struck into the bottom corner from twenty yards.
Simon Bassey's side felt aggrieved just moments later as they were denied a penalty after there were appeals for handball in the Altrincham box.
After a bright response from the Bees, they were undone by the Robins on 15 minutes as Alistair Smith headed home from six yards after Aymen Azaze made a good stop from a free-kick.
The Bees could have halved the deficit on the 30-minute mark as Mason-Clark struck wide after Harry Taylor had forced an error from the Robins 'keeper.
In the boiling sunshine the Bees tried to respond as the half went on but never troubled the Altrincham goal as the final minutes of the half aproached.
However, we were handed a lifeline right at the end of the half, as Courtney Baker-Richardson tapped home into an empty net as he pounced on an error from the Altrincham 'keeper.
At the start of the second half the Bees made a change as Michael Petrasso returned to action, replacing Millwall loanee Sam Skeffington.
We were almost level seven minutes into the second half as Baker-Richardson planted a header inches wide of the post after Alex McQueen's dangerous delivery from a free-kick.
The Bees came close again on the 64th minute as Mason-Clark drilled an effort goalwards which took a deflection on it's way through, forcing the Robins' 'keeper into a brilliant reflex stop.
We should have been ahead with twenty minutes left on the clock as Petrasso's delightful cross found McQueen unmarked, but the Bees number seven could only direct his effort over the crossbar.
Altrincham carried a threat of their own and could have wrapped up the points with ten minutes left on the clock, as they broke quickly from a Bees corner, only for Azaze to make a flying stop to deny Nyal Bell.
But the Bees rallied and found themselves with nine minutes left on the clock as Mason-Clark darted onto a loose ball before cooly slotting home.
However, the drama wasn't over and we found a dramatic winner in the very last minute of the match, as Mason-Clark squared it for Tomi Adeloye to bundle home, sparking wild celebrations on the pitch, the technical area and the press box! It was no more than Simon Bassey's side deserved after a rallying second-half showing.
There was late pressure from the Robins but the Bees dug deep and saw out the match to ensure their first win on the road since October.
Barnet: Azaze, Vaughan, Daly (c), Preston, Beard, Taylor, Skeffington (Petrasso 46'), Kefalas (Adeloye 83'), McQueen, Mason-Clark, Baker-Richardson (Richards-Everton 89').
Unused Subs: McBurnie, Callan (GK).