David Hill kicked Bristol to the most notable win in their Heineken Cup history as tournament favourites Stade Francais suffered a surprise Pool Three defeat.
New Zealander Hill booted four penalties, while centre Neil Brew scored the game's solitary try on 77 minutes to give Bristol a fighting chance of reaching the quarter-finals.
But the game proved a drab affair in cold, wet conditions, with little attacking thrills to enthuse a 10,500 Memorial Ground crowd.
Bristol, in only their second season of top-flight European rugby, resorted to basic rugby, using a vastly-superior pack to smash Stade's resistance.
Although the home side lacked flair or invention behind the scrum, it hardly mattered, because Stade proved even more limited with ball in hand.
It was a shambolic display by the French champions on a weekend when England's Heineken Cup challengers made their presence felt following wins yesterday for Wasps, London Irish and Leicester, while Gloucester beat the Ospreys on Friday night.
Stade, given their magnificent record at Stade Jean Bouin, are unlikely to drop points in Paris during their Heineken Cup campaign.
But if their away form does not improve drastically on today's grisly evidence, then they could struggle to progress beyond the pool stage.
England scrum-half Shaun Perry captained Bristol in the absence of injured flanker Matt Salter, while Roy Winters replaced Nathan Budgett, who damaged windpipe cartilage during last Sunday's defeat against Cardiff Blues.
Stade were led by hooker Dimitri Szarzewski, with two other members of the French World Cup squad joining him on starting duty - Skrela and flanker Remy Martin.
But the French champions travelled without several star players, including Juan Martin Hernandez, Christophe Dominici, Ignacio Corleto and Lionel Beauxis.
Stade's dour approach was in stark contrast to their kit - a fetching khaki and pink number - and they soon found themselves in trouble against a fired-up Bristol pack.
Bristol, despite losing injured wing Tom Arscott after just nine minutes, were not disrupted from their forward-orientated plan for domination.
With England World Cup hooker Mark Regan spearheading the assault up front, Stade struggled for parity, and Hill's opening 18th-minute penalty came after the visitors were pushed off their own ball at a scrum.
Stade then lost number eight Sergio Parisse, who limped off nursing an ankle problem, but his back-row colleague Mauro Bergamasco continued despite suffering a similar injury.
Stade just could not get into the game - Skrela missed penalty and drop-goal attempts - and Hill deservedly doubled Bristol's advantage eight minutes before the break.
Bergamasco failed to reappear for the second period, and there was still no sign of his team-mates turning up either as Bristol maintained a level of control.
Flankers Joe El Abd and Andrew Blowers successfully stopped Stade at source, meaning they were starved of quality possession to let loose a frustrated back division.
Bristol wing David Lemi looked the most dangerous attacker on either side, but try-scoring chances were at a premium as Hill completed his penalty hat-trick entering the final quarter.
Stade could find no way back into the game, and their misery was completed three minutes from time.
A desperate attempt to run possession from deep inside their own 22 predictably failed, and Bristol turned the screw in terms of maintaining field position.
And Brew's clincher came, almost inevitably, from a Stade blunder as he linked with midfield partner Rob Higgitt to touch down and put Stade out of their misery.
Hill's fourth penalty meant the Bristol fans could celebrate, setting up their team for critical back-to-back Heineken Cup appointments with Guinness Premiership rivals Harlequins next month.