Against the run of play Ben Marshall gave Northampton the lead on the half hour mark, netting from close range with a deflected effort after the ball ran free in the area.
Barnet continued to dominate the first half with Yannick Bolasie a constant threat on the left while Albert Adomah created several good chances.
Deen equalised six minutes after the restart when his 20-yard free-kick dipped over the wall and into the bottom corner past a stranded Chris Dunn.
Marshall almost restored Northampton's lead on the hour mark but his great turn and shot was kept out by a reflex save from Jake Cole.
Furlong put Barnet in front in the 68th minute when he finished superbly from 10 yards following a great break on the left by Bolasie.
O'Flynn increased Barnet's lead three minutes later when he capitalised on a short back-pass from Dean Beckwith to beat Dunn.
Barnet are now a point clear of second-placed Dagenham having played a game more, while the Cobblers remain 13th in the table.