With Leicester wrapping up the four-try bonus point just two minutes into the second half, the result leaves Newcastle still six points adrift of London Wasps at the other end of the table.
Leicester withstood a barrage of early pressure to take the lead against a Newcastle side playing primarily for field position.
Teenage fly-half George Ford - the 19-year-old son of Newcastle defence coach Mike Ford - stepped up to slot a penalty from out on the right after a dominant midfield scrum.
Momentum swung further Leicester's way when visiting centre James Fitzpatrick was sent to the sin bin for a high tackle, and within a minute his side were down by double figures.
From a line-out on the left Tigers worked play to the opposite flank, Horacio Agulla breaking free to set up the close-range ruck from which flanker Julian Salvi sniped in for a try.
Ford added the extras, and opposite number Jimmy Gopperth was similarly accurate with a penalty from straight in front to get his side off and running.
The extra man in the backs saw Leicester in for a second try on 22 minutes, this time from centre Billy Twelvetrees as the England Saxons cap rounded off a three-on-two in the right corner.
Another scrummage infringement allowed Ford to slot a second penalty, and more sloppy set-piece work from Newcastle saw a third try for their hosts as an overthrown line-out eventually saw Agulla cross down the left for a 23-3 interval lead.
It took just two minutes of the second half for them to add to that tally and secure the four-try bonus point, turning down a kickable penalty and setting up the catch-and-drive from which Thomas Waldrom rumbled over.
The Falcons finally found their way to the try-line with half an hour remaining through former Tigers academy prop Jonny Golding, who squirmed his way over down the left from close range after a burst from Fitzpatrick.
But with Taiasina Tu'ifua sent to the sin bin for pulling a player back off the ball, the visitors' already slim hopes of a comeback were reduced to dust as Leicester cranked up the power for the closing quarter.
From the very next scrum Waldrom dotted down for a pushover try - his second score of the afternoon - with Newcastle emptying their bench in readiness for Friday's home date with Harlequins.
With their seven-man pack being shunted from pillar to post a sixth Tigers try seemed an inevitability, and it duly arrived as Leicester sucked numbers to the left.
Ford stepped back into the pocket and floated a perfectly-weighted cross-field kick into the right corner for replacement wing Niall Morris - the Irishman catching the ball in acres of space to score.
Replacement flanker Richard Mayhew ploughed over for a late consolation from a ruck to the left of the posts, Gopperth converting, but it made little difference to the eventual outcome.
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