Newcastle centre Jamie Noon ran in a try in the 74th minute – his side's only points in the second half – but Ross's drop-goal in the 71st minute proved to be the difference between the two teams.
The home team held a 20-10 half-time lead and seemed well on their way to recording their seventh win of the 2003/04 season – only for Leeds to produce an inspired second-half showing which saw them rattle up a 18-5 second half win, which, ultimately, secured them the overall victory.
Newcastle had earlier run in three first-half tries, through Kiwis Mark Mayerhofler (No.12) and Daryl Lilley (No.11) and midfielder Tom May, who was playing on the right-wing, with Lilley – in his first match for the Falcons – opening the scoring with a penalty goal in the 21st minute and also converting his try in the 30th minute.
All Leeds had to show for their first-half effort was a penalty from Ross in the 28th minute and a try from scrum-half Alan Dickens, which Ross converted before the break.
Blindside flanker Matt Salter scored Leeds's second try soon after the break, and Ross put the visitors just two points short of the home side with his second goal of the afternoon.
England international Dan Scarbrough eventually put Leeds ahead with a try in the 60th minute, with Ross's conversion putting them clear at 25-20, but Ross delivered the killer blow just over 10 minutes later with his well-taken drop-goal.
Noon gave his side hope with a 74th minute score, but the Leeds defence held out in those frantic final few minutes as the home team threw everything but the kitchen sink at the visiting outfit.
For Newcastle Falcons:Tries: Mayerhofler, Lilley, May, NoonCon: LilleyPen: Lilley
For Leeds Tykes:Tries: Dickens, Salter, ScarbroughCons: Ross 2Pens: Ross 2DG: Ross