Worcester started well enough, although Leicester had been pre-warned by John Wells about their ferocious pack, they still creaked enough to concede two early penalties, which Tommy Hayes slotted fro a 6-0 lead.
But Leicester got into stride and Scott Bemand, Neil Back, and Austin Healey all scored tries to give the Tigers a 17-6 half-time lead.
Then Varndell turned on the style with his trio of tries in the space of twelve minutes early in the second period.
Paul Sampson marked his debut with a late try for the home team, for whom the next fixture at Northampton must be marked down as a possible win.
"We came here with a lot of respect for Worcester, we expected a right ding-dong game and we certainly got that in those first 10-15 minutes," Wells told the club's official website.
"Once we scored that second try the game opened up and certainly in the second half we ended up running away with it."
With Sale Sharks losing, Leicester now sit proudly five points clear at the top of the Zurich Premiership.
For Worcester:Try: SampsonPens: Hayes 2
For Leicester:Tries: Back, Bemand, Healey, Varndell 3Cons: Goode 4