When a flagpole-bending gale blows in off the Exe estuary rugby becomes a different game. This felt like a ‘10-point wind’ in terms of the first-half lead Exeter would have ideally wanted so when the hosts were 12-7 behind at the interval their fate appeared to be sealed. So much for that supposed theory as the Chiefs staged a storming comeback to reach the last eight of this constantly fluctuating Champions Cup campaign.

Bath will be kicking themselves, having been outscored 14-3 with the elements at their back. At precisely the moment they needed to turn the screw their composure increasingly deserted them as Exeter’s self-belief correspondingly grew. If it did not help the visitors’ tactically when their star fly-half Finn Russell departed with an early groin injury, this was a match his remaining colleagues really should have closed out.

Related: Sam Riley edges Harlequins to thrilling Champions Cup win over Glasgow

With Cam Redpath and Ted Hill, scorer of an outstanding solo 50m try, also departing prematurely, the Bath director of rugby, Johann van Graan, admitted his team were “incredibly disappointed” but his Exeter counterpart, Rob Baxter, felt his side fully deserved a victory which sets up a quarter-final against either Toulouse or Racing 92.

“We had full-blooded commitment to be in the game physically from the first minute and we built the game from there,” said Baxter. “It would have been easy for them to think at half-time that they hadn’t done enough. But we’d worked them so hard that I told the lads there would be opportunities in the second half. Hopefully they’ve learned today that the things you do right from the start can add up and win you the game.”

It made for a see-sawing contest from first to last. Bath, having chosen to face the wind initially, lost their hooker Tom Dunn to the sin-bin for a high tackle inside five minutes and Russell lasted barely 15 minutes. Exeter, though, could not translate their early territorial advantage to the scoreboard and the wind-assisted clock was ticking.

It felt like a significant development, then, when Bath worked their way upfield and their dominant maul created a score for Thomas du Toit. Or, at least, it did until Alfie Barbeary fumbled the resulting restart and Exeter’s speedy Ross Vintcent picked up the inviting loose ball to deliver an instant response.

Bath, though, were about to enjoy a bonus of their own. Up went the ball into the swirling skies before falling straight into the arms of Hill on the halfway line. Off surged the tall flanker, showing an outstanding turn of pace, and no one came close to catching him.

Initially Exeter were nowhere near as clinical. The man-of-the-match Manny Feyi-Waboso caused repeated defensive anxiety but on half a dozen occasions the Chiefs could not quite find a way to ground the ball over the line. With kicking, either for goal or diagonally to the corners, also fraught with difficulty, it seemed Bath’s strong maul, breakdown expertise and stout defence would secure them a first Champions Cup quarter-final for nine years.

Leinster set up La Rochelle quarter-final after beating Leicester

Leinster’s Champions Cup title challenge gathered further pace with a 36-22 win over Leicester at the Aviva Stadium as they locked in a repeat of the last two finals against La Rochelle.

The French giants, who edged out the Stormers 22-21 in Cape Town, will return to Dublin for next week’s heavyweight quarter-final, 11 months on from retaining their European crown in fairytale fashion.

Having last lifted the trophy in 2018, a fiercely-determined Leinster cancelled out Handre Pollard’s fourth-minute try as Jamison Gibson-Park’s running off the ball was rewarded with a first-half hat-trick.

Trailing 22-10 at half-time, Leicester capitalised on James Lowe’s sin-binning for a deliberate knock-on as former Munster prop James Cronin was on the end of a 45th-minute maul.

Robbie Henshaw’s intercept effort four minutes later effectively sealed the result while replacements Jack Conan and Charlie Clare exchanged late scores in front of an attendance of 40,775.

A dominant Bulls scored nine tries to secure their spot in the last eight after thrashing Lyon 59-19.

Tries from Sebastian de Klerk, Embrose Papier and Marcell Coetzee gave Bulls the early advantage, with Johan Goosen adding the extras for all three. Martin Page-Relo put Lyon on the board at the half-hour mark as Paddy Jackson converted but Ruan Vermaak extended Bulls' advantage three minutes later with a converted try as they led 28-7 at the break.

An energetic start to the second half saw Lyon hit back through a penalty try, which saw Bulls centre Canan Moodie sin-binned as a result but the hosts quickly added two more tries through Willie le Roux and Papier, with Goosen only able to convert the latter before Thaakir Abrahams crossed for Lyon.

Bulls ran away with the game as David Kriel and Chris Smith crossed within four minutes of each other and Smith kicked the extras before de Klerk added his second of the afternoon with three minutes to go.

Instead, there was to be a major plot twist, beginning late in the third quarter when Greg Fisilau, who had arrived only a few minutes earlier as a replacement, burrowed his way over. Henry Slade’s conversion narrowed the gap to 15-14 and a subdued home crowd were suddenly roaring again.

The volume grew even louder with just under 15 minutes left when a purposeful team attack was finished off from close range by the England flanker Ethan Roots. Slade’s artfully judged conversion was a curved masterpiece and, suddenly, the pressure was back on Bath. With Exeter’s youngsters holding firm, it was the visitors who were ultimately blown away.

Baxter later described it as “a very important game for the club” in terms of fuelling his squad’s confidence and highighted Feyi-Waboso’s all-action contribution. “He’s the closest replacement to a Jack Nowell we could have got. He’s a guy who gets you metres out of nowhere and he’s getting better at it. At least two of our tries came from momentum he generated almost on his own. That shows his value.

“I’ve also told the lads that the quarter-final is a no-lose situation for us. We either get another great experience over in Toulouse or, if Racing win, we get another great day at Sandy Park. And whoever we play we’ll have a day’s more preparation than they will.”