Barkhuizen gave the Shrimps the lead in the 16th minute and added a second through an early second-half penalty to give the Shrimps the advantage before Valdane Oliver pulled one back for the home side in the second minute of injury time.
Barkhuizen’s first goal came from a training ground routine.
Michael Rose floated over a corner to the far post and Barkhuizen was left unmarked as he volleyed past Adam Collin from 10 yards out.
The home side then came back into it with former Blackburn Rovers man Jon Stead, who was a constant threat, heading a left-wing cross from Carl Dickinson inches wide of the left-hand post with Barry Roche beaten.
The Morecambe keeper then did well to parry away a snapshot from Graham Burke and Dickinson was not too far away with a shot from 25 yards that sailed past the left-hand post.
With the home fans becoming increasingly frustrated the Shrimps went on to dominate the closing stages of the first half with Cole Stockton once again leading the Morecambe line superbly.
The on-loan Tranmere man blazed wide after wresting free of his marker when he should have done better but then forced Collin into three fine saves, the best a sharp, reflex stop from a close-range header in the 44th minute.
The Shrimps doubled their advantage 10 minutes into the second half when Louis Laing handled a Rose cross and Barkhuizen made no mistake from the spot.
The home side then enjoyed plenty of possession but rarely troubled Roche, with Ryan Edwards producing a fine performance at the heart of the Morecambe defence.
The only downside to the evening was an Oliver header two minutes into injury time that flew past Roche to provide the only black mark on a fine evening.
The win, which was secured when Roche held an Alex Rodman header in the final of five minutes of injury time, moves Morecambe up to seventh in the table, from 14th.
That makes it 13 points out of a possible 18 away from home for the Shrimps.
Morecambe: Roche, Wakefield, Edwards, Whitmore, Barkhuizen, Jennings, Fleming, Rose, Molyneux (Murphy 76), Stockton (Turner 80), Ellison (Mullin 89). Subs not used: Nizic, Hedley, Massanka
Notts County: Collin, Duffy, Hollis (Audel 62), Laing, Tootle. Burke (Collins 63), Rodman, Richards, Forte, Stead (Oliver 62). Subs not used: Loach, Milsom, Campbell, Aborah.
Booked: Dickinson, Forte