Fly-half Rory Clegg scored all Harlequins' points as the Londoners claimed a hard-fought 14-11 triumph that sinks opponents Worcester deeper into the relegation mire.
Clegg, deputising for New Zealander Nick Evans who failed a fitness test before the match, scored an early try and kicked three penalties - including two in the final 15 minutes - to lead his side to a victory that eases their own relegation fears.
Worcester managed a solitary try of their own through winger Miles Benjamin, as well as two penalties from the boot of Matthew Jones, but came up short and remain just a point clear of Leeds and Sale at the foot of the table.
With so much at stake, it was perhaps predictable that numerous errors punctuated the opening exchanges as both sides wrestled to establish control.
Worcester made the narrowly more impressive start, but it was Quins who hit the front with nine minutes on the clock.
George Lowe laid the foundations with a strong surge up the middle and, although his break was halted, support runners ensured a sustained attack that finished with Clegg being driven over on the right from close range.
He was unable to add the extras to his own score as he screwed his conversion well wide.
But Worcester did not trail for long and hit back two minutes later when Chris Latham completed a swift attack, his pass sending in Miles Benjamin on the left to touch down - like Clegg, Jones failed with the conversion.
Quins thought they had scored a second try in the 20th minute when Lowe chipped ahead and beat the defence to the ball in goal, but referee Martin Fox ruled he had knocked on in attempting to touch down.
Having survived a couple more scares, Worcester earned the chance to edge ahead in the 32nd minute, only for Jones to see his attempted penalty swerve just wide of the target.
With the sides level at the break, it was the hosts who started the second half in more positive fashion with the home fans at the Twickenham Stoop urging their charges on.
But Quins were unable to turn possession and territory into points and were made to pay on 50 minutes when Worcester broke the shackles to move ahead for the first time.
After three well-constructed phases of play, Quins conceded a penalty in front of their posts and Jones slotted the resulting kick.
Indiscipline quickly allowed Harlequins the chance to restore parity with Clegg landing his first penalty after Worcester killed the ball.
Some poor kicking from hand then saw the hosts put themselves under needless pressure and they fell behind again in the 63rd minute, Jones booting an impressive kick from 40 metres on the angle after the referee spotted hands in a ruck.
Again the lead proved short-lived with Worcester soon penalised for coming in at the side and Clegg levelled things up at 11-11 with 14 minutes remaining.
The youngster then made himself the match-winner in the 70th minute, booming over a towering penalty from halfway to restore Harlequins' lead - and this time they did not relinquish it.
Pens: Clegg 3
Pen: Jones 2
Harlequins: 15 Mike Brown, 14 David Strettle, 13 George Lowe, 12 Jordan Turner-Hall, 11 Tom Williams, 10 Nick Evans, 9 Karl Dickson, 8 Tom Guest, 7 Will Skinner (c), 6 Chris Robshaw, 5 George Robson, 4 James Percival,3 John Andress, 2 Matt Cairns, 1 Ceri Jones.
Replacements: 16 Tani Fuga, 17 Aston Croall, 18 James Johnston, 19 Lewis Stevenson, 20 Chris York, 21 steve So'oialo, 22 Rory Clegg, 23 Nils Mordt.
Worcester: 15 Chris Latham, 14 Chris Pennell, 13 Dale Rasmussen, 12 Sam Tuitupou, 11 Miles Benjamin, 10 Matthew Jones, 9 Jonny Arr, 8 Kai Horstmann, 7 Pat Sanderson (c), 6 Tom Wood, 5 Craig Gillies, 4 Greg Rawlinson, 3 Tevita Taumoepeau, 2 Chris Fortey, 1 Matt Mullan.
Replacements: 16 Adam Black, 17 Aleki Lutui, 18 Olivier Sourgens, 19 Graham Kitchener, 20 Chris Cracknell, 21 Ryan Powell, 22 Calum MacRae, 23 Alex Grove.
Referee: Greg Garner
Assistant referees: Alan Biggs, Andy Watson
Television match official: Roy Marfleet