Rhodri Williams, Scott Williams and Jordan Williams supplied the tries and Rhys Priestland scored 18 points as the Celtic visitors completed a thrilling victory at the Twickenham Stoop.
Quins were second best throughout and had it not be for the the brilliance of Brown, who crossed twice and was their heartbeat from start to finish, they would have lost more emphatically.
Both of the finishes were high-class and Brown must have all but guaranteed his position as England's first choice full-back for the autumn internationals against Australia, Argentina and New Zealand.
On the domestic front the prognosis is less healthy, however, with Quins losing what on paper should have been the easiest game of their Pool Four campaign with French heavyweights Clermont and Racing Metro to come.
The result mirrors their poor form in the Aviva Premiership with two defeats in five matches leaving them seventh.
Only seven minutes had passed when the Scarlets ran in the opening try with a steal by Aaron Shingler at the back of a line-out beginning the move.
Space opened up on the right and it was expertly exploited by the Welsh region with Priestland delaying his pass until the crucial moment to enable Rhys Williams to sprint over.
The conversion by Priestland was followed by two penalties to leave Quins, who were struggling to gain any sort of foothold in the game, trailing 13-0 inside the opening quarter.
Nick Evans landed a penalty to briefly stem the flow of points, but when the Scarlets probed the right wing once more - this time through the marauding Shingler - their line was in danger of cracking for a second time.
Only last-ditch defending held the Scarlets up over the whitewash, but in the next passage of play Quins exploded into life with Brown leading the fightback.
The England full-back counter attacked from his own line with Danny Care and Tom Williams continuing the move until the cover arrived as the try beckoning.
Quins would not be denied in the 33rd minute, however, when Evans sent a crossfield kick to Nick Easter who gather and passed to Brown.
There was still work to do but Brown's finishing was clinical as he stepped inside the cover and raced home, with Evans converting.
Just as the Premiership club appeared to have clawed their way back into the game, the Scarlets struck again with a superb solo try from Scott Williams.
The inside centre, starting on the halfway line, darted between Ben Botica and Rob Buchanan and dummied Care before winning the race to the line. Priestland's conversion restored the 10-point lead.
Quins enjoyed a productive spell early in the second half when visiting prop Samson Lee was sent to the sin bin for stamping on Care and Evans sent a drop-goal between the uprights.
But even with the extra man, confusion and uncertainty returned to their ranks and after Priestland and Evans exchanged two penalties each, the Scarlets produced a third try.
Prop Joe Marler had the ball ripped from his grasp by Scott Williams and moments later wing Jordan Williams was racing down the left wing, evading four tackles before diving over with Priestland converting.
Brown responded with a brilliant solo finish that saw him plot a mazy run to the whitewash and when Quins pushed for an undeserved draw they were foiled by a try-saving tackle from Liam Williams on Paul Sackey.
- Sports & Recreation
- Rhys Priestland
- Rhodri Williams