Second half strikes from Deen, Furlong and O'Flynn gave the visiting side a win that sends them top of the table and leaves Town with just seven points from their opening six league games.
Ben Marshall had given the home side the lead with a defle
cted first half effort but his passionate performance was in vain as the supporters vented their frustration at manager Stuart Gray.
Cobblers had gone into the game without the injured Steve Guinan, so Adebayo Akinfenwa and Gary Mulligan were paired for the first time in competitive action up front.
Robbie Threlfall and Luke Boden were selected by Gray to make their home debuts.
On loan Liverpool full-back Threlfall was given the unenviable task of marking in form Barnet man Albert Adomah and the Cobblers man was under pressure early on as the flying winger flashed a fantastic ball across the box.
No Barnet man was able to get a touch to what was an inviting ball, though, and fortunately for Town the scores remained level.
The men from Underhill had the first attempt on goal after an opening 25 minutes with little action, as evergreen front man Furlong guided his header way wide.
The next player to register any sort of effort was Cobblers midfielder Ryan Gilligan who, after two goals in his last two games, took on a free-kick 25 yards from goal but directed it miles into the away fans.
However, just moments later Marshall did much better as he charged towards goal and fired a shot into the away net.
The on loan Stoke City winger picked up the pieces after Boden had seen his own run halted and Cole had no chance with Yakubu sticking out a foot which only served to beat his own keeper.
The visitors quickly responded by winning a free-kick in opposition territory and, although he looked offside, it wasn't given and Furlong guided a free header over the bar.
With 42 minutes on the clock and Cobblers set to go in at half time with a lead, Adomah again beat Threlfall and sent in a teasing cross which was headed inches wide by left winger Yannick Bolasie.
On a night when neither team seemed to have brought their shooting boots, both Boden for Cobblers and Adomah for Barnet fired wayward shots at goal early in the second half.
Marshall, having been the only man to actually hit the target up to the 50th minute, then tested Cole with a smashing volley which was well saved by the Barnet custodian.
His effort was bettered just a minute or so after as visiting left-back Deen curled a brilliant free-kick past a helpless Chris Dunn to restore parity.
It was a fine finish from the Barnet man and one which resulted in the home faithful upping the volume and the Cobblers increasing their advances towards the away goal.
Marshall whipped in a free-kick which caused a melee on the Barnet line but the away side somehow survived with no Town player able to force the ball over the line.
The tricky winger, Town's best player on the night, was causing more problems on 61 when he weaved his way into a shooting position but saw his strike parried away from danger by Cole.
The Barnet keeper was certainly busy and he was called into action again when Gilligan broke through on goal but let the ball slip away much to the relief of the visiting centre-backs.
After going in at half-time a goal down, the Barnet turnaround was complete on 69 minutes as
Furlong guided a superb volley over Dunn.
The Cobblers keeper was beaten for a second time on the night despite only seeing two Barnet shots hit the target.
Unbelievably, the third effort directed between Dunn's upright also found the target as Gray's men conceded once again. This time it was substitute O'Flynn who netted after Dean Beckwith misjudged a long ball.
Boden had a late header saved by Cole but that was the best Town could muster in what was a below-par performance.
