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A remarkable comeback against the English aristocrats at Ravenhill was accompanied by the even more remarkable news that Aironi had shocked Pool 4 pace setters Biarritz.
If the Ulster legions had remained confident that Bath could be beaten despite an early 15-3 deficit in Belfast, few would have predicted Biarritz' demise at the hands of a side previously without a win in this competition or in any other.
"It was a tough match and we're delighted with the result," said Ulster head coach McLaughlin.
"We lost our first two lineouts but, after that, we settled and we put pressure on Bath's possession. Our set scrum was good too and I was happy with the tempo we tried to play at. We've talked in the last month about raising the tempo of our game and take our opportunities and I thought we did that.
"At 15-3 down, we knew that if we could just get ourselves back in the game, we could get then the points to move ahead and hold on. And all credit to the boys, we did that.
"Even in the second half there were a few mistakes but you can talk about that but you can't fault the effort and the endeavour.
"The attitude the guys had was just brilliant. You only have to look at the Andrew Trimble tackle in the last play of the game to see what this competition means to us.
"That was a smashing win by Aironi, too. We've experienced Biarritz and we know how good a side they are.
"It means there's everything still to play for in next week's game in Bath for both teams. I'm sure we'll get another great game of rugby next week.
"Next week's a completely different game, though. Our mindset has to be that we're going there with a positive attitude. We have to go there and play because we need the points. We need to keep building our game, building our tempo and make sure that we're playing the kind of rugby we want to play.
"The physicality and the warfare out there was immense. It was very intense and it's a short week when you think about the effort these guys put in."
Ulster began proceedings at Ravenhill expecting a big win from Biarritz and knowing quarter-final qualification would depend heavily on their double header with England's first-ever European Champions.
A little bit too much festive spirit appeared to be running through their veins early on, though, as McClauglin's men gifted the visitors a 15-3 lead with 22 minutes played.
A brace a mistakes from the hosts handed Bath two early tries, with Ian Humphreys' interception and Adam D'Arcy's misjudged catch giving Bath a dream start in Belfast.
Jack Cuthbert raced fully 80 minutes for the first on seven minutes, before England skipper Lewis Moody picked up superbly and then handed off Nigel Brady for the second 15 minutes later.
Those early setbacks may have unsettled the famous Ravenhill faithful but they didn't have the same effect on their heroes in white.
Having dominated possession without reward, Ulster stuck to their task, scoring a try of their own when Predie Wannenburg intercepted on halfway with 34 minutes gone.
The South African No8 showed the covering defence a clean pair of heels in sprinting home from just inside the Bath half after expertly picking off an ill-timed pass.
Fly-half Humphreys then narrowed the gap to just two points at half-time with a conversion and a second penalty from fully 50 metres and it was his boot that did the damage in the second period.
Humphreys showed his class and character to put his early mistake behind him as he slotted three successful second-half penalties to just the one from Bath's Olly Barkley.
Ulster had to hold on at the end as Bath pressed in the final few minutes but a shuddering tackle from Trimble ended their charge and demonstrated the commitment to the cause that McLaughlin spoke so highly of.
