Rhodri Williams, Scott Williams and Jordan Williams all crossed for Simon Easterby’s side at the Twickenham Stoop.
Mike Brown scored two tries for the Aviva Premiership side, but the Welsh region held on to record a famous win.
The Scarlets had lost nine of their previous 10 Heineken Cup fixtures including all six pool fixtures last season, but you would not have believed that after watching the opening 40 minutes at the Twickenham Stoop.
Easterby’s men were ahead as early as the seventh minute when scrum-half Williams scorched over.
Rhys Priestland was at the centre of the move, linking up with Kristian Phillips before his inside pass sent Williams over in the corner.
The Wales fly-half added the conversion to put the Scarlets on the front foot.
Priestland nudged the visitors further ahead with two quick-fire penalties on 10 and 15 minutes as Harlequins seemed shell-shocked by the lightning start.
Nick Evans got the Londoners up and running on the scoreboard with a routine penalty and they finally found a spark on the half hour mark when the lively Brown, returning Danny Care and Tom Williams combined.
But, rather than backing himself to finish in the left-hand corner against Davies, the wing looked for the inside pass and Jonathan Davies covered well to avert the danger.
Yet Brown made no mistake two minutes later. Liam Williams was deceived by Evans’ chip over the top and the England full-back capitalised to race in to the left of the posts before Evans’ conversion reduced the deficit to three points.
However, the Scarlets responded on the stroke of half-time courtesy of Scott Williams’ solo effort. Liam Williams started the move by gathering a high ball and bulldozing his way through three tackles.
Still in their own half, the Scarlets spread the ball wide and Scott Williams dummied to beat Brown and galloped home for a wonderful score.
Priestland converted and the away side had a 10-point advantage at the interval.
But the visitors were dealt a blow early in the second period when prop Samson Lee was yellow carded for a stamp on Danny Care’s face.
Evans immediately capitalised with a fine drop goal before Priestland nudged the Scarlets further clear with two penalties.
Yet there was still plenty of life left in this thrilling contest. Evans added two more penalties before the Scarlets grabbed a third sensational try.
With little space to work in, Jordan Williams showed superb footwork to dance along the touchline before cutting inside Brown to score.
But Harlequins kept fighting and Brown scored his second try of the afternoon to keep the tie alive and it needed an excellent tackle by Liam Williams to deny Paul Sackey a try with two minutes remaining as the Scarlets held on.
