But they are well aware they will need to improve after they were forced to rely on a late try by replacement Lucas Lyons four minutes from time to salvage a draw at Cammi Rugby Calvisano.
Similarly, Newcastle came within minutes of becoming the first English team to be beaten by Bucharest Wolves.
Trailing 12-10, it looked as though Bucharest might hold on for a famous win until full-back Tom Catterick slotted a winning kick four minutes from time. There will be concerns, however, over the fitness of captain Alex Crockett who limped off with an injury.
The result was a cruel blow for Wolves head coach Lynn Howells, a veteran of European campaigns with Pontypridd, Cardiff and Celtic Warriors, who will now relish the chance to claim their first win of the campaign.
Bucharest claimed their biggest score in Europe when they faced Calvisano last season, winning 42-27, when they scored a club record six tries.
However Calvisano were more than a match for Brive in Round One and would be celebrating a shock win had fly-half Kelly Haimona not missed with four kicks, including a last-minute penalty.