But they had to wait until the final minute of normal time to clinch the important bonus point when winger Paul Sackey ran 70 metres to finish a move that had taken them from their own line.
After a dominant opening 20 minutes the champions, who are chasing their third successive title, were made to battle every inch of the way by a Worcester side desperately battling the threat of relegation after one year in the top flight.
Ultimately, the second-half sin-binning of Worcester flanker Pat Sanderson proved the pivotal moment with Wasps scoring 17 vital points during his 10-minute absence.
Wasps, 45-24 winners over Saracens last week, looked set for another big win as they tore into Worcester from the start.
England winger Josh Lewsey, playing in the centre, opened the scoring inside three minutes, snatching the ball from the base of a ruck and scything through the Warriors' defence for a superb solo try, converted by fly-half Mark van Gisbergen.
They were denied a second in the 10th minute when full-back Tom Voyce looked to have clearly grounded the ball after being driven over, only to see his effort disallowed.
Van Gisbergen kicked a 14th-minute penalty when Worcester killed the ball in front of their own post but the visitors defended stoutly against the superior pace and explosive power of the champions.
Worcester disrupted the suspect Wasps line-out, stealing three of their first-half throws, and fly-half James Brown relieved the pressure several times with his astute kicking.
Brown opened Worcester's account with a cool 40-metre drop goal just before the interval and Warriors, against the run of play, drew level five minutes into the second half.
Van Gisbergen's clearly-telegraphed pass was gratefully intercepted by Warriors centre Thomas Lombard who was left with a clear run to touch down between the posts, presenting Brown with an easy conversion.
Lombard should have had another try three minutes later when his centre partner Dale Rasmussen split the Wasps defence wide open with a weaving run but after he had done all the hard work Lombard spilled the final pass with the line at his mercy.
Wasps were clearly rattled but after Sanderson was shown the yellow card for persistent breakdown infringement by Worcester, van Gisbergen's penalty put Wasps back in front at 13-10 in the 56th minute.
Brown missed a second drop-goal attempt and, while Sanderson was off, Wasps struck twice more with England back-row men Lawrence Dallaglio and Joe Worsley both diving in for tries, converted by van Gisbergen, after the Worcester defence was stretched to breaking point.
Just when it looked as though Wasps would be denied their bonus point, they ended a spell of Worcester pressure by bursting out of defence for Sackey to score what could prove to be an important fourth try.
But Worcester refused to roll over and they grabbed their second try, through left-wing Ben Hinshelwood converted by Brown, deep into injury time.
For London Wasps: Tries: Lewsey, Dallaglio, Worsley, SackeyCons: Van Gisbergen 3Pens: Van Gisbergen 2
For Worcester Warriors:Tries: Lombard, Hinshelwood Cons: Brown 2Drop: Brown