The semi-final win puts the Midlanders within 80 minutes of next season's Heineken Cup competition – quite a feat for a side who secured just one win from their first eight games of the English league season.
Andy Goode kicked 13 points for the home side, with Geordan Murphy, Neil Back, Jaco van der Westhuyzen and Harry Ellis all chipping in for a try apiece.
Leicester's dominant pack also earned recognition in the shape of a penalty try, awarded in response to a very creaky Quins scrum.
Leicester raced into a 13-0 after 24 minutes with two penalties from Goode.
The outstanding Van der Westhuyzen then charged down a clearance from Andy Dunne to dot down and gift Goode an easy conversion kick.
Dunne made amends for his touch-finder by winning a kick-and-chase race with Gavin Duffy to score and convert.
Goode answered with a penalty and the Tigers surged further ahead after the penalty try was awarded at the stroke of half-time.
A 23-7 half-time lead quickly became 40-7 with three Tiger tries within 10 minutes of the second period.
Back notched up a trademark try from the tail of a driving maul, Murphy then finished off a sweeping move sparked by hooker George Chuter and continued by centre Daryl Gibson.
Austin Healey then collected a shank of a clearance kick before feeding the impressive Ellis who scampered home to collect the Tigers' fifth try.
Quins managed to pull themselves off the ropes and scored three tries of their own, Dunne showing the way by slicing through a gap to score his second try of the game.
Ugo Monye then collected a smart Will Greenwood pass before galloping into space to score, and creator Greenwood then turned finisher after getting on the end of a Quins move to give the scoreboard an air of respectability.
But this was always going to be Leicester's day, and Van der Westhuyzen made sure the home side had the last word by striking a neat drop-kick through the poles in injury-time.
But Quins need not despair just yet – they get a second bite at the Heineken Cup cherry when they face Montferrand in the Parker Pen Final this Saturday.
For Leicester Tigers: Tries: Van der Westhuyzen, Penalty try, Back, Murphy, EllisCons: Goode 3Pens: Goode 3DG: Van der Westhuyzen
For NEC Harlequins:Tries: Dunne 2, Monye, GreenwoodCons: Dunne 2, Jarvis