General manager John Gibbs said: "It was a massive win for us. We played some great attacking football against a very good side."
Longwell Green are in fifth place, with games in hand on all the teams above them.
They got off to a great start, scoring a second-minute goal through Dave Parnell.
However, Bideford equalised on 75 minutes as Kevin Squire netted from close range.
But Longwell Green won it at the death, when Cole chased down a back-pass and got the better of the Bideford goalkeeper.
Brislington paid the penalty for poor defending at Welton Rovers as the game ended 2-2.
Justin Bishop's chip put Brislington ahead in the fifth minute, but Welton levelled through Dean Evans.
The same player then put Welton in front before the break, but Jason Hughes headed the equaliser against his old club with 10 minutes remaining.
Bristol Manor Farm went ahead in the 10th minute of their home game with Dawlish, thanks to Troy Simpson. Luke Clark made it 2-0 with a 25-yard free-kick and then added a third with 55 minutes gone.
His side needed the cushion as Gary Fisher and Dean Stevens pulled goals back for the Devonians.
Bishop Sutton got back to winning ways with a 3-1 victory at Hallen, where they took the lead through Rob Smart.
Hallen equalised just before half-time with an Andy Cook penalty, but goals from Darren Hawkins and Leon Britton ultimately gave Sutton their win.
Bitton were a goal down after 20 minutes at Wellington, as Jack Adams scored from the penalty spot.
However, Andy Black's side recovered and levelled when Joe Chandler scored his first goal for the club.
Wellington looked to have won the game with a late Shane Kingston strike, but Brandon Barnes scrambled an equaliser right at the death.
In the First Division, Hengrove Athletic scored through Ricky Charlton, from the penalty spot, Danny Guibarra and Sam Williams in a 3-3 draw at Chard Town, whose equaliser came in injury-time.
Oldand Abbotonians were 5-1 home winners over struggling Minehead with goals from Matt Huxley (2), Dan Bryant and Spencer Thomas, and an own goal.
Keynsham Town went down 2-0 at home to Odd Down, while Cadbury Heath had to settle for a 1-1 home draw against Portishead.
Clevedon United were 1-0 home winners over Roman Glass St George.
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