Five tries secured a bonus point, and left the Londoners five points adrift at the bottom of the table, facing a crisis situation.
Early tries by ex-Quins star Pat Sanderson and centre Ben Hinshelwood gave Worcester a dream start, establishing a 14-0 ahead inside 16 minutes.
Samoan Siaosi Vaili provided the clincher from close range midway through the second half, before his fellow replacement Lee Fortey then guaranteed an extra point with Worcester's fourth try and James Brown completed the rout in injury time.
Brown booted four conversions to finish with 13 points and Quins could only manage a 20th minute Luke Sherriff touchdown, converted by Jeremy Staunton, in reply.
Worcester were fired-up and dominant for most of the game against a Quins team that really needs a new direction
Worcester made the early running, with Powell prominent around the forward fringes, and they went ahead in classic set-piece fashion after 10 minutes.
Lock Craig Gillies took a clean line-out catch 15 metres out from the Quins line, and his fellow forwards drove on relentlessly, enabling skipper Sanderson to claim an impressive touchdown that Brown converted from wide out.
It got worse for Quins just five minutes later, and this time they were undone from inside the Worcester half as Powell sparked a thrilling counter-attack.
His pace and angle split Quins' defence open, and the move ended with Scottish international Hinshelwood touching down in the corner. Brown again landed a difficult conversion.
Quins were visibly rocked, but their reply came before a lively opening quarter had ended.
Prop Ceri Jones powered forward with line-out possession, and although he was tackled, the supporting Sherriff made the most of his chance, with Staunton's conversion halving the deficit.
Worcester tightened up defensively after Sherriff punished them, and they had chances to extend their lead before the break, but the Warriors sacrificed a couple of kickable penalties before Brown rifled a 30-metre chance wide.
Trailing by seven points at the break, Quins needed to start the second period by establishing supremacy, but they were immediately put under pressure and had full-back Gavin Duffy sin-binned for slowing the ball down.
Worcester strived to make their temporary one-man advantage count, and it required some desperate last-ditch defending from Quins when home centre Thomas Lombard dived for the corner.
French international Lombard was narrowly denied a try, yet Worcester kept battering away before their perseverance was rewarded.
Hooker Ben Daly crashed through Quins' defensive front-line, causing sufficient damage for Vaili to power over. Brown once again added the extras.
Worcester then turned the screw in terms of territory, going flat out for a bonus point that arrived four minutes from time when Fortey sent a 7,000-strong Sixways crowd wild.
Quins' heads had dropped, all the life had gone out of their team, and James Brown scurried over to compound their misery in the final move of the game
For Worcester:Tries: Sanderson, Hinshelwood, Vaili, Fortey, BrownCons: Brown 4
For NEC Harlequins:Try: SherriffCon: Staunton