But they still managed to contain a Saracens team who had picked up try-scoring bonus points in their four previous Premiership matches, and restrict them to a measly two touch downs.
The Saracens coach, Steve Diamond, was happy to admit that his side's approach had been less than expansive. "I was satisfied with the four points," he said. "We have been able to score tries in our opening four Premiership matches but had one win to show for that style of play.
"And Bristol are going to be a difficult team to beat here. I am just happy we don't have to come to the Memorial Stadium for another 12 months. I came here as a player perhaps 12 or 13 times and was never on the winning side."
For five minutes of yesterday's match - the opening five - Diamond must have felt that nothing was going to change. The muscular, mobile centre Sam Cox found himself on the end of a great cut-out pass from Bristol's outside-half, Jason Strange, and shimmied and dummied his way over for his team's only try.
Unfortunately, Strange missed the conversion as well as three penalties which might have put a different complexion on the outcome, although Saracens always looked too well organised to lose.
They were far superior in the scrum, where Cobus Visagie was able to take advantage of a front row which was denied the services of Mark Regan, who is recovering from injury. The powerful South African prop practised some of the dark arts of front-row play, bamboozling the referee, Rob Debney.
The line-out was more of a playground than a workplace for Saracens. Only desperate defending by the home side, where Cox was always prominent, kept the score down.
Not that Bristol's defence was all that shipshape when Saracens cruised in on the left through Ben Johnston for their opening try, which Glen Jackson converted to ease them ahead after 10 minutes.
They were in front and there they stayed. As Diamond said, it was not pretty to watch, but at least the modest crowd (by Bristol's standards this season) of 7,068 was treated to some attractive rugby during the half-time interval.
A tag rugby match between teams of boys and girls produced some cracking tries - two of the three scored by girls were blistering efforts which saw the boys' defences being stretched and ultimately outgunned.
It was almost a disappointment when the main event reconvened for the second half. At least Bristol tried to make a better fist of things and there were a couple of enterprising moves, one of which saw the hooker, Saul Nelson, get over the line. He was adjudged to have knocked on in the act of touching down. Apart from a second penalty for Strange, that was pretty much that for the home team.
Saracens exerted even more pressure, pretty much camping in the home side's half. They were helped by a string of penalties as Bristol grew desperate.
They eventually crumbled to concede a second try when Ben Skirving, a temporary scrum-half, helped himself to the ball when it was presented at a ruck and strolled over unopposed. A subsequent Jackson drop goal sealed Bristol's fate and left them pointless.
Bristol: Try Cox; Penalties Strange 2. Saracens: Tries Johnston, Skirving; Conversions Jackson 2; Penalties Jackson 2; Drop goal Jackson.
Bristol: B Stortoni; L Robinson, R Higgitt, S Cox, V Going (M Contepomi, 40); J Strange, S Perry (J Rauluni, 40); D Hilton, S Nelson (N Clark, 71), D Crompton, R Winters, G Llewellyn, M Salter (capt), J El Abd, G Lewis (D Ward-Smith, 71).
Saracens: T Castaignède; B Johnston, K Sorrell, D Harris (B Russell, 69), P Bailey,; G Jackson, K Bracken (A Dickens, 62); K Yates (N Lloyd, 61), M Cairns (S Byrne, 61), C Visagie, S Raiwalui (K Chesney, 56), I Fullarton, H Vyvyan, A Sanderson (T Randell, 56), B Skirving (D Seymour, 80).
Referee: R Debney (Leicestershire).