Lemi opened the scoring for Bristol early in the second half
Bristol (0) 20
Tries: Lemi, Blaney, Clarke
Harlequins (0) 7
Bristol remained on course to challenge for a Heineken Cup quarter-final spot in the new year after scoring three second-half tries to subdue Harlequins.
After a scoreless first half, Samoan wing David Lemi made the breakthrough with a try on the resumption.
But Quins hit back with a converted try from Tom Williams before Bristol regained the lead with a second score from replacement David Blaney.
David Hill's penalty stretched the lead before Alex Clarke's try sealed it.
The victory puts Bristol ahead of Stade Francais in pool three and level on points with Cardiff with just two games to go.
The first half saw few scoring opportunities but Hill missed two chances to break the deadlock on 23 and 26 minutes.
Quins fly-half Adrian Jarvis hit the crossbar from 30 metres soon after and the home side injected a bit of life into the game when England scrum-half Shaun Perry made a 25m jinking run.
The visitors had scrum-half Danny Care yellow-carded for persistent infringement just before the break and Bristol took advantage when wing Anthony Elliott linked up with Rob Higgitt to put Lemi clear to score in the corner.
Despite being down to 14 men, Quins responded quickly through full-back Williams, who pounced on a kick through from acting number nine Simon Keogh.
Blaney, who had only been on the field for 10 minutes, came up with the ball after the forwards bundled over while Hill's penalty put Bristol six points clear.
Prop Clarke then scored in injury time to make sure of the victory although Blaney was stretchered off late on while England hooker Mark Regan and number eight Dan Ward-Smith both suffered injuries.
Bristol coach Richard Hill:
"We should have kicked on and got the bonus point but if I was told we would have three wins out of four at the start of the competition, we would be delighted to be equal top.
"Having said that it was points dropped, although we are not a team that scores many bonus points as our game has been built on set-piece and defence and the attacking game will, I hope, develop over the next couple of years.
"With the possession and the chances we had, to come away without a bonus point has taken the edge off the win a bit."
Bristol: Arscott; Elliott, Higgitt, Brew, Lemi; Hill, Perry; Crompton, Regan, Hobson; Winters, Hohneck; Salter (capt), El Abd, Ward-Smith.
Replacements: Blaney, Clarke, Llewellyn, Blowers, O'Riordan, Strange, Cox.
Harlequins: Williams; Strettle, Luscombe, Turner-Hall, Keogh; Jarvis, Care; Croall, Fuga, Nebbett, Percival, Spanghero, Hala'ufia, Skinner (capt), Guest.
Replacements: Botha, Jones, Evans, Volley, Davies, So'oialo, Masson.