A try by flanker Jon Dunbar pulled the hosts level in the dying minutes of the game, before his captain Hugh Vyvyan broke down the right wing only to be caught agonisingly short.
The Falcons skipper duly flung a one-handed pass to the supporting Mark Mayerhofler who spilled the ball across the line in the last action of the game.
In retrospect, Newcastle could have guessed this wasn't to be their day from the opening minute.
Local star Jamie Noon took to the field to celebrate a record 47th consecutive Premiership appearance and 3,680 minutes of continuous Premiership rugby. But the centre was forced to abandon the latter record after 3,681 minutes when he was felled by Leicester's Henry Tuilagi.
Newcastle then lost full-back Joe Shaw who was stretchered off after a collision in the 18th minute.
Next, Leicester star Jaco Van der Westhuyzen went over for the first of his brace of tries when he charged down a clearance by Mayerhofler.
Somehow, the Falcons managed to regained their composure and soon sent winger Michael Stephenson in at the corner.
Newcastle's Dave Walder and Leicester's Andy Goode added the kicks to leave the hosts trailing just 13-11 at the break.
The Falcons refused to dwell on their early losses and soon took the lead after replacement Daryl Lilley chipped ahead, Vyvyan collected and Tom May went over in the corner.
The Tigers responded with a strong run from Henry Tuilagi and Van der Westhuyzen appeared at his side to take the pass and dart over for his second try.
Goode converted to move Leicester back into the lead 20-18, and when former England star Neil Back crashed over soon afterwards, the Tigers had edged 25-18 ahead.
But Newcastle broke out with a flowing move in which Mayerhofler and Lilley cut through the middle and Lilley's reverse pass sent in Dunbar.
Walder levelled the scores with the conversion before the highly-animated hosts set out on the move that spawned that nightmare-inducing injury-time miss.
For Newcastle Falcons:Tries: Stephenson, May, DunbarCons: Walder 2Pens: Walder 2
For Leicester Tigers:Tries: Van der Westhuyzen 2, BackCons: Goode 2Pens: Goode 2