Fijian winger Vereniki Goneva clinched a bonus point win for Leicester with a stunning solo try in the final minute of a disappointing start to the defence of their Aviva Premiership title at Welford Road.
Leicester's other three tries came from Adam Thompstone, David Mele and Jordan Crane but they were way below par for most of the game and had to fight off a spirited second half fightback by Worcester.
Trailing 18-3 at half-time and then 25-3, Worcester scored tries through Chris Jones and Josh Matavesi to put themselves back in the game before Goneva clinched a win which maintained the Tigers 100 per cent record at home to the Warriors.
Leicester, who announced record season ticket sales of 14,700 on the back of last season's Aviva Premiership triumph, fielded four new signings.
Half-backs Mele and Ryan Lamb started, while Neil Briggs and Owen Williams were on the bench. Four of their British and Irish Lions - Tom Youngs, Dan Cole, Geoff Parling and Tom Croft - also started.
Worcester's new boss Dean Ryan, back in the Premiership after an absence of four years, handed debuts to five new signings - forwards Jonathan Thomas, the captain, Mike Williams and Jeremy Becasseau and backs Ignacio Mieres, Jeremy Su'a.
Leicester totally dominated the first half and turned round with an 18-3 lead thanks to tries from winger Thompstone and Frenchman Mele and eight points from the boot of Lamb.
Leicester, however, would have been disappointed with the lead considering the amount of possession they enjoyed. They lacked a cutting edge and Lamb missed a conversion and two penalties.
Worcester's only points came from a penalty by Mieres, who also missed one, from long range, in the fourth minute.
Two minutes later Lamb put Leicester ahead with a penalty after a fabulous counter attack by Thompstone but failed with another from further out in the 10th minute.
Leicester stretched their lead in the 13th minute with a cracking try from Thompstone, who picked up a grubber by full-back Niall Morris to score in the left corner.
Lamb missed the conversion but, after centre Anthony Allen had just failed to hang on to an interception for a possible try, the fly-half produced a fabulous piece of skill to send centre Dan Bowden storming into the Worcester 22.
It came to nothing but Lamb made it 11-0 with his second penalty in the 23rd minute.
Worcester made a rare foray into the Tigers 22 in the 31st minute thanks to a storming run by number eight Semisi Taulava, who then ruined his good work by knocking on following a ruck.
Mieres put Worcester on the board with a 34th minute penalty before Lamb missed his second.
But, with the game meandering to half time, Lamb started a move that led to Leicester's second try in the 40th minute, Mele scoring from Crane's pass after a bullocking run by prop Logovi'i Mulipola with Lamb converting.
Worcester's problems mounted three minutes after the break when lock Mike Williams was sin-binned for a body-check on Lamb after the fly-half's chip ahead.
And three minutes later Leicester number eight Crane scored from a line-out and drive, which Lamb converted to make it 25-3.
Lamb's attempted kick to his left winger on his own 22 went straight into touch and led to Worcester's first try.
From the line-out Worcester drove hard, switched the ball left and, after a pile-up on the line, replacement Jones squeezed over with Mieres adding the conversion.
And after Leicester failed to score from a line-out and drive centre Matevesi put Worcester back in the game with a try from nowhere, his diagonal run to the line taking Leicester by complete surprise. Mieres missed the conversion.
Right on time winger Goneva scored a fabulous solo try to clinch the bonus point for Leicester, with Owen Williams wrapping things up with the conversion.