The visitors had surged into the lead with tries from South African flanker Warren Britz after opting to kick for touch from a close range penalty – and then England 'A' wing Michael Stephenson, who grabbed their second.
Two penalties and a conversion from the boot of England Sevens star Ben Gollings took their lead to 18-3, as a Tim Stimpson penalty was all Leicester had to show for their efforts.
But coach Dean Richards' men fought back, with a try from Italian fly-half Ramiro Pez – on his Premiership debut – getting them back into the game after charging down a clearance kick.
That was followed by a try by youngster John Holtby, after Stimpson's second penalty had further reduced the deficit.
Newcastle then significantly had key forwards Mark Andrews and Hugh Vyvyan both sent to the sin bin in the second half, and the Tigers took full advantage.
Stimpson had converted both tries, and the Tigers wrapped up the match with a try from lock James Hamilton in the 56th minute.
A third penalty for Gollings gave Newcastle the consolation of a bonus point, but it was the hosts who took the lion's share of the points in this encounter. The scorers:
For Leicester Tigers:Tries: Pez, Holtby, HamiltonCons: Stimpson 2Pens: Stimpson 3
For Newcastle Falcons:Tries: Britz, StephensonCon: GollingsPens: Gollings 3