Daniel Nardiello put the hosts in front with a 45th-minute penalty before David Worrall sealed victory eight minutes from time.
That sent the Shakers back up to eighth after they surrendered an 11-match unbeaten run at Morecambe on Tuesday.
Although winger Albert Adomah and striker Craig McAllister were busy for Barnet, the Bees failed to forge a clear opening throughout.
The Shakers took the lead as Nardiello sidefooted home with aplomb after Mark Hughes tripped Morrell in the box.
Ryan Lowe then headed over from a cross by fellow substitute Richie Baker before Worrall nipped in to seal it eight minutes from the end, with Hughes shown a second yellow card at the death.