Defending champions Leinster joined rival Irish province Munster in qualifying for the quarter-finals of the European Cup after notching up a hard-fought 23-16 victory over Glasgow on Sunday.
Leinster, on 20 points in Pool 3 after four victories and a draw, will now face Montpellier at home in the final round of pool matches next weekend to book themselves a home tie in the knock-out phase.
"I am delighted to get the result today even though there were imperfections in the performance. But the players deserve to be proud of what they did," said Leinster coach Joe Schmidt.
"It was every bit as tough as I expected. We knew it was going to be a battle of attrition and that's how it turned out.
"We wanted to up the tempo if we could but it was difficult on a heavy pitch. I knew they would go hard in the collision area and they were very good in that area - they made life very difficult for us and it was fairly brutal at times."
English champions Saracens all but assured themselves of a berth in the last eight, new England call-up Owen Farrell nailing five crucial penalties to help see Biarritz off 20-16.
Saracens now have 18 points and travel away to Italian club Treviso next week, while Biarritz host Ospreys in a far trickier fixture.
In Glasgow, Duncan Weir and Leinster counterpart Jonny Sexton and then Fergus McFadden traded first-half penalties.
Leinster opened the second-half with a Rob Kearney try, the full-back latching onto a kind bounce from a Sexton cross-kick to cross the line, McFadden adding the extras.
Weir claimed a third penalty to keep his team in the hunt, but McFadden stretched the lead again with his second three-pointer.
Replacement scrum-half Colin Gregor then bundled over in the corner and Weir hit the tricky touchline conversion to draw the scores level at 16-16.
But Leinster hit back with a crucial turnover in Warriors' territory, and Kiwi-born Ireland international scrum-half Isaac Boss spun over from close range for a try under the posts.
With five minutes remaining, Leinster flanker Sean O'Brien was yellow-carded, but the Irish team rebuffed a revitalised Glasgow side to hold on for the win.
In the day's late game, five Farrell penalties proved decisive, allied with an early Ben Spencer try.
But the game could have gone either way with evergreen scrum-half Dimitri Yachvili scoring all Biarritz's points, including an opportunistic charge-down try.
Saracens captain Steve Borthwick said he was "very pleased with the win", turning his thoughts immediately to the away trip to Italy next weekend.
"Treviso are a very good side and have challenged every team they've played," he said. "It's going to be a good challenge."
Two-time champions Munster reached the quarters for the 13th time on Saturday with a battling 26-10 win over Castres.
Four-time champions Toulouse clinched a four-try, bonus-point 24-3 win over Connacht which gave them a two-point lead at the top of Pool Six over Harlequins who defeated Gloucester 20-14.
In Pool Two, Cardiff Blues beat London Irish, the win moving Cardiff to 17 points, the same as Edinburgh who had needed a last-minute drop goal from replacement fly-half Phil Godman to secure a 27-24 win over Racing Metro on Friday.
Cardiff face Racing in their final match next weekend as they look to reach the knock-out stages for the first time since the 2008-09 season.