Prop prospect Simon McIntyre grabbed an opportunist try to help sink Worcester for the second time this season as Wasps opened their account in the LV= Cup.
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The 21-year-old former England Under-18 player, who scored his first Wasps try in October's 10-6 win over Worcester in the Aviva Premiership, notched his second as they bounced back from last weekend's 22-17 away defeat by Cardiff Blues.
Winger Jack Wallace and replacement scrum-half Charlie Davies scored the other Wasps tries with third-choice fly-half Tommy Bell contributing 13 points with a five-from-five goalkicking display.
Worcester replied with tries from centre Alex Grove, right wing Andy Short and replacement left wing Ben Howard, with fly-half Joe Carlisle landing two conversions.
Wasps' shadow pack - hooker Tom Lindsay was the only first-choice forward on duty - provided a solid foundation with a dominant scrum.
With Tom Palmer and Joe Launchbury away on England duty and Marco Wentzel injured, Wasps borrowed Josh Thomas Brown from Championship side London Scottish.
They went ahead in the seventh minute, capitalising on a poor lineout throw by Wasps hooker Ollie Hayes after full-back Hugo Southwell's superb long-range kick found touch inside the visiting 22.
Hayes' throw cleared everyone before being gratefully collected by McIntyre at the tail end of the line and he ran in unchallenged to leave Bell a simple conversion.
Carlisle missed a 10th-minute penalty for Worcester before Wasps were temporarily reduced to 14 men.
Scrum-half Jonah Holmes was sin-binned by Welsh referee Rhys Thomas for failing to release the ball after being tackled as he fielded a kick near his own line.
The Warriors capitalised with two tries in a three-minute spell.
Carlisle turned the ball inside to put Grove over in the 27th minute but Worcester, with a two-man overlap on the right, were denied a second try by Matt Everard's excellent tackle on Short.
The visitors maintained the pressure, moving the ball from right to left before full-back Ernie Claasens joined the line to provide the final pass for Short to touch down in the corner.
Carlisle made amends for two earlier misses by landing the conversion from the touchline.
Bell's 31st-minute penalty cut the deficit to two points and, seven minutes later, he booted Wasps into a one-point lead with a superbly struck penalty from the left touchline.
The Warriors replaced prop Ceri Jones with Ryan Furniss at half-time but Wasps continued to dominate the scrums and, six minutes into the second half, they forced back-pedalling Worcester to concede a penalty, despatched by Bell.
Wasps were denied a second touchdown when Tom Varndell, the Premiership's leading try-scorer, was forced into touch a metre from the line.
But the home side produced a stunning move to increase their lead in the 63rd minute.
Moving the ball quickly from a lineout, Bell found Varndell and his quickfire pass released Wallace who burst over in the corner, with Bell again successful from the touchline.
Worcester retaliated with a 72nd-minute try in the left corner by replacement winger Ben Howard, converted by Carlisle.
But, two minutes later, Davies collected a kick by Worcester's replacement fly-half Andy Goode and produced a diagonal run for the corner to score an excellent solo try but stand-in kicker Lee Thomas missed the conversion.