Created by an inspired assist from Shane Horgan, O'Driscoll's score with the very last play of the game means that Leinster can now afford to lose their last pool game against London Irish at Twickenham on Saturday and still reach the knockout stages.
If they manage to stay within seven points of London Irish, who surprisingly lost 31-22 to Welsh side Llanelli, to secure a losing bonus point, they will top the pool. However, another win will see them guaranteed an important home draw in the quarter-finals.
Coach Michael Cheika admitted that not delivering a home quarter-final in his five seasons in Dublin was a major regret. "I realise I haven't delivered it to the fans, and we're really committed now so we need to win and make sure we pay them back."
Without a match for three weeks due to freezing conditions, Leinster took a while to get into their stride and only led 7-0 at the break. They eventually forged ahead with tries from Isa Nacewa and Gordon D'Arcy, however, Brive responded with a couple of tries of their own, and it was only 20-10 going into the last minute.
However, Horgan was put into space about 20 meters from the Brive line and he produced a brilliant one-handed reverse pass which O'Driscoll gathered without breaking stride to dive over for the crucial fourth try. "It wasn't going well for us," added Cheika, "but we stuck at it and showed good belief. When the play needed to be executed right, the players backed themselves and got it done."
Munster also got it done albeit in less fraught circumstances when they traveled to Treviso in Italy and registered a crushing 44-7 victory which also puts them in pole position to book a home game in the quarter-finals.
If the 2006 and 2008 champions get the better of Northampton at Thomond Park on Friday, they will top the pool, and even the highly unlikely prospect of a defeat will see them through as one of the best runners-up.
Given that French champions Perpignan had lost in Treviso and that Northampton had only won by three points, coach Tony McGahan was understandably pleased with the outcome. "I'm delighted to get that result, others have come here before and struggled. As for the Northampton game on Friday, we'll be in an excellent state of mind for that one."
Munster had wrapped up the bonus point by half-time with tries by Denis Hurley, Keith Earls, Donncha O'Callaghan and Paul Warwick, and they were able to take their foot off the pedal during the second half before Earls again and sub Donnacha Ryan added further tries.
Ulster retain a slim chance of reaching the knockout stages following their 21-13 win against Edinburgh in atrocious conditions at Ravenhill, however, their prospects weren't improved by Stade Francais's narrow 15-13 victory over Bath.
Ulster now need to turn Bath over at the Recreation Ground on Saturday, securing a winning bonus point along the way, and hope that Stade lose in Edinburgh, but realistically, a place in the Challenge Cup last eight now appears to be their best bet.
Darren Cave and Isaac Boss scored tries for the northern province while Ian Humphreys landed three penalties and a conversion in a contest that was spoiled as a spectacle by constant wind and rain.
Meanwhile, whatever happens this weekend, Connacht are guaranteed a place in the quarter-finals of the Challenge Cup following their 20-10 victory over Montpellier in last Friday's pool-deciding game at the Sportsground.
That's not the only good news as the scheduling dice has rolled nicely for Michael Bradley and his players who travel to bottom-placed Madrid on Saturday in search of a sixth win out of six in the competition as well as a bonus point which could earn them a prized number one ranking going into the knockout stages.
While a win in Madrid, which will secure a home quarter-final in early April, would appear to be a formality given both the Spaniards' inexperience and Connacht's 46-6 stroll against the same opposition in Galway earlier in the season, the bonus point could turn out to be highly significant.
If the number one ranked side going into the last eight wins their home quarter-final game, then they are assured of a home semi-final as well. At the moment, London Wasps need a bonus-point victory over Racing Metro in Paris on Thursday to grab that top ranking, but if they slip up, Connacht are best placed to come through as the number one team.
If all will be revealed this weekend, what is currently certain is that Connacht have cut an impressive swathe through a demanding Challenge Cup pool despite some contrasting poor form in the Celtic League. Winning on the road in Montpellier gave them a chance, and then an outstanding double success over English Premiership club Worcester set up last Friday's key game.
Although Montpellier decided not to play their France internationals, Francois Trinh-Duc and Fulgence Ouedraogo, as well as the goal kicking Argentine, Federico Todeschini, they weren't at the Sportsground just to make up the numbers.
Having won the toss and chosen to face a strong wind in the first half, Connacht battened down the hatches superbly and were level 3-3 at the break. "Delighted. It was one of the best halves of rugby we've played," said Bradley. With scrum-half Frank Murphy in superb form, the job was finished with tries by wings Liam Bibo and the fleet-footed Fionn Carr while Ian Keatley converted both and added a second penalty.