A teasing free-kick delivery by Lewis Knight was met by the Havern, who escaped Sean Reid inside the box, to nod home from eight yards as his side held on for a crucial victory.
The team from the Horsfall set up with plenty of pace in attack and caused their hosts some problems early into the game.
Issac Marriott, who never stopped running for 90 minutes and the link between midfield and attack, tried his luck from 25 yards but it flew over the bar.
After watching Tyrone O’Neill drag a shot wide from a similar position, the Avenue were hitting the channels well, with both Omar Sanyang and Brad Dockerty supporting Knight and winning free-kicks in good positions. But it was Harry Boyes, who continues to impress during his loan spell, crossing the ball into the area but the referee blew his whistle to give handball against former Avenue man Ben Hedley.
Knight stepped up and curled the ball towards the penalty spot and Havern rose the highest to glance a header into the back of the net, sparking celebrations from those wearing amber and black.
Alun Armstrong’s side grew into the game and, five minutes later, hit the woodwork twice in 60 seconds.
Erico Sousa came off his wing with the ball, running across the pitch, finding Adam Campbell on the left flank and his cross was headed by striker Dan Maguire from eight yards against the bar.
As the Avenue tried to clear the danger, O’Neill grabbed a loose ball, worked possession onto his right foot and curled an effort, from 25 yards, towards goal but Dan Atkinson produced an unbelievable fingertip save to deny the striker as the ball thundered off the underside of the bar and into the goalkeeper’s hands.
Maguire was forced off with an injury as was replaced by Luke Charman for Darlo, but that didn’t affect the Avenue’s gameplan as they nearly doubled their advantage.
Marriott found Knight who ran at the defence and the striker fired a low right-footed shot from 20 yards which was pushed away by goalkeeper Johnny Saltmer.
After the restart, the Avenue continued to look for a quick counter-attack to hurt their opponents but it was Darlington FC who came close to an equaliser.
From a similar position to the goal, Sousa delivered a free-kick into the box, but Boyes was the first to react and crucially flick the ball away from the head of Louis Laing.
The Avenue were struggling to get out of their own half, but all the play was in front of them and with nine men behind the ball, Bradford continued to frustrate the home side.
O’Neill was dropping deeper to get the ball and after looking up, he spotted an unmarked Campbell on the edge of the box. Just as he got a shot away, Mark Ross and Luca Havern bravely threw their bodies at the ball to take the pace out of his effort making it an easier save for Atkinson.
The Avenue number one was forced into another fine save as midfielder Joe Wheatley, who’d been kept relatively quiet by the impressive Marriott, drove forward and rather than passing, he hit a low right-footed strike from 20 yards, which was well saved by Atkinson.
After a cheeky chip from substitute Jarrett Rivers being saved by the outstretched hand of Atkinson, the Avenue got the opportunity they wanted. Dockerty set himself up, 25 yards from goal, and with a gap between the two defenders, the number nine fired an excellent strike which was tipped against the bar by Saltmer.
Into additional time, the Avenue remain organised and disciplined. After seeing O’Neill’s effort fly over from 25 yards, Bradford were tested one final time. They cleared the ball away but Hedley controlled the ball, made a great connection from distance, and his shot brushed the top of the bar to the relief of the visitors.
Darlington FC: Saltmer, Hedley, Watson, Laing, Atkinson, Sousa, Reid, Wheatley (Hudson 86), Campbell (Rivers 64), Maguire (Charman 31), O’Neill
Subs not used: Minter, Storey
Bradford (Park Avenue): Atkinson, Ross, Boyes, Marriott, Havern (c), Windass, Toulson, Hibbs, Dockerty, Knight (Clee 76), Sanyang
Subs not used: Downing, Huffer, L.Lyons
Goal: Havern (15)
Yellow cards: Havern, Hibbs
Referee: Jonny Urwin