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Top scorer Andy Bishop gave Bury a 40th-minute lead with his 14th goal of the season before defender Efe Sodje sealed the Shakers' fifth win in six games in the 85th minute.
The game got off to a slow start until, in the 14th minute, a corner led to Notts County striker Delroy Facey somehow clearing a glancing header by Ryan Cresswell off the line.
Barry-Murphy then hit a superb inswinging cross from the right which found Andy Morrell at the near post but the Bury striker was unable to direct the ball goalwards.
The visitors were enjoying plenty of possession but were unable to create a chance of note in the first half as Bury continued to look the likeliest scorers.
Winger Elliott Bennett had a goal harshly disallowed in the 22nd minute as he challenged Jamie Clapham to head home Mike Jones' left-wing cross.
Mike Edwards then misjudged a long ball by Bennett, allowing Morrell to nip in front of goalkeeper Kevin Pilkington and the home crowd was fuming not to see a penalty awarded.
But Bury deservedly broke the deadlock as Jones hit a searching ball towards Bishop, who was up front on his own.
His marker, Edwards, could only nod the ball down towards his own goal and Bishop charged onto the loose ball to beat Pilkington with a delightful lob from 25 yards.
The Shakers remained on top after the restart as left-back David Buchanan played the ball inside for Jones, who fizzed a low shot across the face of goal.
The Magpies finally threatened following a Myles Weston cross from the left byline but Facey's close-range header was scrambled clear and Matt Hamshaw handled trying to fire the ball back in.
The hosts were comfortable for the remainder of the second half, though, and Jones curled a shot narrowly wide with ten minutes left.
Sodje then lashed home his fifth of the season from Barry-Murphy's late corner.