It came after Richard Butcher's cross was overhit at Harrison and he let it slip straight through his fingers.
An inept first half display saw the Magpies go in at the break a Jason Puncheon goal down.
An improved second half display meant Notts were full value for their point in a scrappy game that rarely got going.
That meant there were no changes to the side who won 2-0 at Accrington Stanley with Andy Parkinson also fit but only on the bench, Somner and Parkinson replacing Rob Austin and Stef Frost on the bench respectively.
Against a Barnet side who before Saturday had gone ten league games unbeaten, Notts started sharply with Saturday's goalscorers Craig Lindfield and Lawrie Dudfield immediately bright up top.
Kicking down the infamous Underhill slope, the NCM big battle between Lee Canoville and Puncheon immediately got going as Canoville angered the Barnet bench with a thunderous - and late - early challenge on Puncheon, but the referee correctly issued just a warning.
Puncheon then popped up with a fizzed effort that Notts keeper Kevin Pilkington could only parry but gather at the second attempt.
Having won the first corner of the game, Notts had their first attempt after ten minutes as the corner was worked short through Butcher and Neil MacKenzie, before it was released to Paul Mayo who hit at goal off target with Lindfield attempting a late deflection.
After 13 minutes Butcher won another corner with some determined play that
Saturday's loan hero Lindfield showed his inexperience immediately after when given his first senior booking, by Premiership referee Andy D'Urso, to follow his first senior goal at Accrington, for a foul on Kenny Gillet.
Lindfield and Dudfield were beginning to cut isolated figures as Notts seemed to play more like they did under McParland's predecessor Steve Thompson with several long balls that went to nothing.
However, Notts were getting forward and laid on by Dudfield, Myles Weston got into the game to force a fourth corner in the first eighteen minutes, but that came to nothing once again.
Mayo brilliantly cleared a moment of real danger from Paul Fairclough's men when he headed away under real pressure with winger Michael Leary ready to pounce at the back stick from a good Nicolau cross.
The game started to get scrappy with neither side stamping their authority on proceedings, and both playing a direct style, with half of the first period gone.
The Magpies, in their changed blue strip, certainly could not be faulted for their work rate, despite failing to reach the heights of Accrington or Wrexham as half-time drew closer.
Striker Adam Birchall worked the ball well and laid in Puncheon who, under no pressure and from outside the box, powered an effort past Pilkington to leave him no chance.
For those who saw Lindfield's excellent finish at Accrington, this one was arguably better and although Barnet had hardly been threatening themselves, Notts could have no complaints following a poor first period.
Following just a minute of added time, Notts went into the break behind at Underhill to a fantastic strike from Puncheon, but it was the overall performance that would give McParland cause for concern.
Notts immediately sought to rectify it and a stroke of luck got them back into
A patient build-up saw Weston force his way down the wing and switch it to Canoville who neatly released Butcher.
His cross was over-hit to Harrison but he let it slip into his own net for what may even go down as an own goal rather than Butcher's sixth of the campaign - one for the dubious goals panel!
The Magpies came close to an immediate second as a MacKenzie corner saw defensive duo Stephen Hunt and Tann, aswell as Dudfield, stretch to touch home but all only narrowly avoided a flick that would have surely resulted in a goal.
Following the incident Bees defender Sagi Burton collided with Hunt, with some Notts players claiming Burton had stamped on the Magpies captain, but D'urso hadn't seen anything and after treatment Hunt was able to carry on.
Fitness doubt Liam Hatch was the first substitute to enter the action after passing a fitness test, replacing Nicolau as Fairclough pushed a further man forward.
Following the much needed early equaliser, Notts were largely getting the better of their hosts in the second half, and despite not yet being perfect were easing their football back into their play.
Barnet got themselves moving forward again and Birchall saw a tame effort comfortably gathered by Pilkington from just inside the box.
A second Barnet change came as Leary departed for Ashley Carew with twenty minutes left.
Puncheon was foolishly given far too much room again after 74 minutes when midfielder Josh Wright worked his way through and gave it to him, and he again powered a long-range effort at goal that could only be fisted away by Pilkington, taking no risks.
McParland made his first change with fifteen minutes left withdrawing the hard working Weston for Hector Sam.
Indeed, all three possible substitutions were made in a matter of minutes, with it unclear whether McParland was pushing for a winner or shutting up shop, as Somner also entered for an injured looking Hunt and Austin McCann came on for the quiet Lindfield.
Tann took Hunt's armband with Canoville moving inside and Silk to right-back.
Pilkington had to be at his best to deny Barnet after Puncheon brilliantly created an opening for Birchall in behind the Notts backline but the former Mansfield stopper blocked well.
Notts had a chance of their own when the ever-involved Butcher crossed well but Dudfield couldn't quite reach it, and Somner's follow-up was easily blocked and cleared.
Dudfield, who seemed to grow as the game wore on, weaved his way through a couple of challenges and hit a good effort at goal that was deflected over for another Notts corner - that again coming to nothing.
But it was the hosts who finished stronger and deep into added time they were still pressing for a winner and a series of set-pieces troubled Notts with Wright hitting one loose ball at goal that a Magpies defender got the slightest of touches to deflect for a corner with a winner seemingly certain.
Notts survived the late onslaught, and with a creditable point from a freezing night in North London eamed, Notts made it three games unbeaten ahead of the league break - and an FA Cup tie with Histon - at Meadow Lane on Saturday.