The action was fast and furious from the kick off with both sides playing with pace and width. Strangely, the game remained scoreless until the 17th minute when a great off load from Quins wing Chris Banfield saw young flanker Will Boyde open the scoring. Craig Evans converted for a 7-0 lead.
Evans then made it 10-0 on 29 minutes with a well struck touchline penalty before opposite number Josh Lewis replied three minutes later to get Llanelli moving.
They may have been behind but on home turf, Llanelli were creating plenty of chances. A couple of opportunities slipped by, the Llanelli backs profligate at times, but eventually, Duane Eager touched down in the left hand corner. Lewis added the extra two as the sides ended the half all square.
The second period saw the Quins explode out of the blocks, centre Dylan Morgans bursting through for a try within a minute of the restart. Evans again converted from the touchline and with both outside half's in fine kicking form, two more Lewis penalties to one from Evans made it 16-20 with 17 minutes remaining.
Two yellow cards for the Quins and one for Llanelli had interrupted the game but with a man advantage, Llanelli looked like they would be able to overturn their deficit.
But too many unforced errors began to creep into their game while Lewis was forced off injured to be replaced by Nic Damjanovic.
Wing Gareth Walters took over the kicking duties and in the 68th minute brought his team back to within a point.
But when given two further chances to win the game for Llanelli, Walters saw his kicks slip wide as the Quins held on in what was a great advert for Premiership rugby.