Wasps started the game well with fly-half Danny Cipriani impressing in the opening stages ahead of Wednesday's announcement of England's Elite Player Squad for the Six Nations.
Cipriani found a gap in the Leicester defence and his break set up the well-worked move which saw Van Gisbergen cross the line.
Leicester's Toby Flood, another number 10 hoping to impress the England selectors, missed a kick at goal before nailing a penalty on 14 minutes.
Wasps threatened to score soon after when Scott Hamilton's attempted kick from deep was charged down but the home defence was superb and the danger was cleared.
Cipriani's penalty made the score 8-3 but Wasps had no answer as Leicester's forwards simply blew them away.
The Tigers had a series of scrums near the Wasps line just before the break and after visiting prop Tim Payne was sin-binned, the ball was spread wide with accuracy and Murphy touched down in the corner.
Murphy (left) and Hamilton celebrate Leicester's first try
Leicester's set-piece dominance continued after the break and they produced a passage of play leading up to the second try that would have warmed the freezing home support.
A Tigers scrum travelled 15 metres before Flood fired a penalty touch to near the corner flag. The resulting line-out was ideal and as the ball went down the line, Tuqiri ghosted past Wasps lock Simon Shaw in midfield to score - although there was a lot of doubt as to whether the former Australian international grounded the ball cleanly.
Wasps were a beaten team and Flood extended the lead with his second penalty while referee Romain Poite awarded a penalty try to Leicester after another series of scrums near the try-line.
Payne should have got a consolation but he dropped the ball with the line at his mercy following a superb last-gasp tackle from England hopeful Dan Cole.
Tuqiri ran in for his second with 17 minutes left and Leicester comfortably closed the game out for a fine win.
Leicester head coach Richard Cockerill:
"I am so proud because we've beaten a very fine team after working so hard all week to get the game on.
"On average we do 15-20 scrums a week, but I've played in France and we have some Argentine guys here so our scrummaging experience is good.
"The scrum has been the foundation of our recent victories and young Dan Cole has played his part.
"He is a local lad who wants to play for his local club and I don't want him getting bogged down in talk of England.
"Dan is only 22 and has lots to learn. But he is playing well, and it's up to the England coaches."
Tigers wing Lote Tuqiri: "Playing behind a pack like ours is sensational, and it was tremendous to get the tries after being here for seven weeks.
"This is one great club and I'm already having a good time, even with this weather."
Wasps rugby director Tony Hanks: "I was pleased with Danny Cipriani's performance at fly-half.
"He is back to good form, and while it was a bit ambitious not taking that penalty in the first half when we led 8-3, that is now the reason we go home empty handed.
"We didn't take a couple of penalties when we should, then we lost Tim Payne to the bin and that set us back.
"Scrums are hugely important, and you have to be on your mettle there. We'll go away and work very hard on that area.
"We've got a few injuries and a few guys to come back, but we also need to get working on our scrummage in the coming weeks.
"You learn and improve by playing, not just working on the scrum machine."
Leicester: Hamilton; J Murphy, Hipkiss, Staunton, Tuqiri; Flood, B Youngs; Ayerza, Davies, Cole, L Deacon, Parling, Newby, Moody, Crane. Replacements: Tuilagi for J Murphy (53), Vesty for Staunton (64), Grindal for B Youngs (64), Stankovich for Ayerza (64), Chuter for Davies (60), R Harris for Cole (67), Croft for Newby (58), B Deacon for Crane (64).
Wasps: Van Gisbergen; Sackey, Jacobs, Waldouck, Lemi; Cipriani, Robinson; Payne, Webber, Broster, Shaw, Skivington, Hart, Matthews, Ward-Smith. Replacements: Varndell for Lemi (65), Honeyben for Robinson (65), Ward for Webber (61), Taulafo for Broster (50), Veale for Shaw (53), Leo for Matthews (52). Not Used: Bocca, Walder.
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