The Quins looked certain losers on Saturday when they trailed 15-3 with barely 20 minutes remaining.
But they burst from their slumbers to score two converted tries - the first from Sam Smith, and the second a penalty try - to maintain their run.
Worcester took an early lead when Andy Goode kicked a 25-metre penalty in the fourth minute after a strong run by Marcel Garvey had put the visitors on the back foot.
In the early stages, both sides tried to move the ball at every opportunity but poor passing and the concession of frequent penalties ensured that neither could build up any real momentum.
Referee Chris White awarded a flurry of penalties from set scrums after spotting various minor infringements.
After 17 minutes of disjointed play, Nick Evans tied up the scores by kicking a simple penalty after Worcester were penalised for dragging down a maul.
Goode soon restored the home advantage with another routine penalty.
The Warriors then produced a fierce scrummage drive which sent the Quins pack backwards for almost 15 metres and in so doing the visitors conceded a penalty.
From five metres inside his own half Goode fired over a monumental effort to give his side a 9-3 lead.
Quins were dealt a further blow when star wing Ugo Monye limped off with an ankle injury and was replaced by Seb Stegmann just before the half-hour mark.
Harlequins' Mike Brown produced the only run of any note in a very disappointing first half but after beating two home defenders on a 30-metre run deep into the Worcester 22, the Quins once again gave away yet another penalty.
Worcester deservedly held the interval lead and they built up early pressure in the second half thanks to a huge clearance kick from Goode.
At a set scrum Quins gave away yet another penalty and Goode made no mistake to extend the Warriors' advantage to 12-3.
Worcester then went close to scoring the first try of the game when Neil Best charged down Karl Dickson's clearance kick, but the subsequent drive from the home side came up narrowly short.
The Warriors were not to be denied a score though, as Goode dropped a 25-metre goal with 25 minutes to go.
Worcester dominated the third quarter of the game but suffered a set-back when influential skipper Kai Horstmann departed with a leg injury.
They still led 15-3 but almost immediately their hopes of clinging on were hit by the first try of the game.
Against the run of play in the 59th minute, Evans produced an exquisite pass to send Smith on a 30-metre run to the line for a try. Evans converted and the gap was down to five points.
Harlequins were revitalised and built up sustained pressure.
Time after time they drove for the home try-line but the Warriors defence held firm.
There was a succession of five-metre scrums at which Worcester conceded penalties, and with seven minutes remaining home flanker Jake Abbot was sent to the sin bin.
That cost Worcester dearly as from the next scrum the Quins were awarded a penalty try which Evans converted to put them into the lead for the first time and secure what had seemed an unlikely victory.
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