The game swung in the visitors' favour when home keeper Lee Harrison was injured in just the second minute.
Going up to collect a high ball, he fell awkwardly and was stretchered off the pitch with an ankle injury.
Substitute Danny Naisbitt conceded a goal in the tenth minute and things went from bad to worse for the home side when Jason Rees scored.
A Paul Holmes cross into the box saw Kevin Hill left with a free header and he made no mistake from six yards out.
Torquay suffered their own injury blow when Rees who had impressed, also limped off with an ankle knock.
Barnet were gifted a way back into the match when an unnecessary handball in the box gave them a penalty.
Darren Currie's spot-kick was brilliantly saved by Stuart Jones and all seemed lost for the home side, especially when The Gulls went up the other end and Graham slotted in the third with two minutes to go before the interval.
To their credit Barnet fought back and an own goal by Ryan Green followed by a farcical goal, with the keeper lying on the ground, the referee did not blow for a foul and Wayne Purser rolled the ball into the unguarded net.
This did not prove to be enough and Barnet's decade long stay in the league came to an end.
Blackpool's 3-1 victory at Feethams propelled them into the play-offs as Rochdale could only manage a scoreless draw at Plymouth.
The result sees Steve McMahon's side scrape into the play-offs in seventh place where they will face Hartlepool.
A two goal burst by Ibrehre secured Leyton Orient's play-off place, as they beat Macclesfield 2-0 away.
It was a mixed affair for the promoted sides as Chesterfield cantered to a 3-0 home win over Halifax, who had already confirmed their survival.
Yet it was a hungover performance by Brighton who crashed to a 3-0 away defeat at Shrewsbury and Cardiff fell to a 3-1 loss at Hartlepool.
Click below for a detailed report when available:
Barnet 2 Torquay United 3
Carlisle United 0 Hull City 0
Cheltenham 3 Southend United 1
Chesterfield 3 Halifax Town 0
Darlington 1 Blackpool 3
Exeter City 0 Lincoln City 0
Hartlepool 3 Cardiff 1
Macclesfield 0 Leyton Orient 2
Mansfield Town 1 Scunthorpe 0
Plymouth Argyle 0 Rochdale 0
Shrewsbury Town 3 Brighton 0
York City 1 Kidderminster 0
