The hosts looked like they had clenched a crucial win when their Scottish fly-half Gordon Ross slotted a penalty in the last minute of regulation play – but the Falcons were not finished, and Dave Walder managed to navigate a 50-metre penalty through the posts in the dying seconds to secure a share of the spoils.
Leeds got off to a great start when former Springbok André Snyman pounced on a mistake by Falcons fullback Joe Shaw to poach a try in the ninth minute which Ross – on for the injured Phil Christophers – managed to convert.
Newcastle hit back with three penalties and a drop-goal from fly-half Walder to take a sudden lead.
Ross soon stole back the advantage with a place-kick of his own, before his captain Tom Palmer – a lock – stepped inside Walder to race in from 30 metres for a converted try on the half-hour mark.
Walder managed to pull back yet another penalty goal to leave his side within sight of the hosts, and the players went to the break with the score at 17-15 in Leeds' favour.
The Falcons torn into their hosts early in the second half and Walder and Warren Britz combined to put centre Tom May in at the corner after some good pressure from the visiting pack.
Back came Leeds, however, with centre Tristan Davies racing through, and Ross converting to win back the lead in the 53rd minute.
But to the horror of the home crowd, Newcastle again went back in front when Walder's inside pass found Michael Stephenson in space and in full flight, and the winger cruised through for a try, which Walder converted to set the scores at 27-24 after 60 minutes.
Ross levelled the scores with a long-range penalty with two minutes of normal time left, before taking the lead with another in the 80th minute.
In a frantic finale, Leeds were penalised for not releasing, and Walder lined up his monster kick that secured the draw.
Leeds actually had a chance to win the game moments later, but Ross was unable to emulate Walder's effort – his last-gasp penalty effort from half-way falling agonisingly short.
For Leeds Tykes:Tries: Snyman, Palmer, DaviesCons: Ross 3Pens: Ross 3
For Newcastle Falcons:Tries: May, StephensonCon: WalderPens: Walder 5DG: Walder