Bury boss Chris Casper's disastrous week continued as Barnet made it four straight league wins.
Casper, who offered to quit after Bury were kicked out of the FA Cup over an ineligible player, saw Richie Baker put his team ahead with a penalty.
But Nicky Bailey headed an equaliser from Richard Graham's cross and Adam Birchall netted the winner after Graham's shot was blocked.
Barnet's Dean Sinclair was sent off in the 84th minute for a second yellow.
Barnet: Flitney, Devera, Charles, Yakubu, King, Cogan, Bailey, Sinclair, Graham, Birchall (Hessenthaler 86), Puncheon (Hatch 72).
Subs Not Used: Jaimez-Ruiz, Warhurst, Nicolau.
Sent Off: Sinclair (84).
Booked: Sinclair, Charles.
Goals: Bailey 7, Birchall 18.
Bury: Fettis, Woodthorpe (Kennedy 56), Challinor, Scott, Brass, Buchanan (Youngs 81), Mattis (Barry-Murphy 52), Baker, Pugh, Blinkhorn, Hurst.
Subs Not Used: Grundy, Fitzgerald.
Booked: Woodthorpe.
Goals: Baker 3 pen.
Att: 1,959
Ref: L Probert (Gloucestershire).