Harlequins (17) 24
So'oialo led the way for Harlequins
Tries: So'oialo 2, Keogh
Cons: Malone 3
Bristol (7) 18
Tries: Lemi, Arscott
Pens: Hill, Strange
Samoan scrum-half Steve So'oialo notched a try in each half as Quins survived a Bristol fightback.
So'oialo darted in to score near the posts but Bristol were back in it after Josh Taumololo burst clear and David Lemi touched down on the left.
Tom Guest caught a cross-kick to send Simon Keogh clear on a 20-metre run.
England U-20 centre Jordan Turner-Hall raced within sight of the line before finding So'oialo to score, but Tom Arscott's try gave Quins a late scare.
Quins director of rugby Dean Richards said rising star Jordan Turner-Hall is not ready for England duty just yet.
The teenage centre shone in the 24-18 win over Bristol, but Richards said: "He needs to add a bit more to his game, and it will come."
Bristol boss Richard Hill agreed, saying: "He's a powerful young man and gives Quins a lot of 'go-forward'.
"But as you've seen (with England), it can be a step back if you get involved and it's the wrong game."
Hill added: "While I'm disappointed, I thought our defence was fairly strong.
"We're starting to play some competitive rugby against some competitive sides."