There was utter elation for Glasgow as they earned a European Cup quarter-final place at the 18th attempt, mixed with horrible embarrassment for Leicester as they tumbled appallingly to what is the heaviest margin of defeat in a competition match at home across the Tigers' 137-year history.

The PRO12 champions of 2015 brought their fast-paced daring style to Welford Road, using the full width of the pitch, for the first time since 2001, and with reminders in the circumstances of qualification up for grabs of the awful day they were swatted away 90-19 here in a play-off for a quarter-final spot back in November 1997.

The suffering was all Leicester’s on this occasion – with nothing to play for, in competition terms, as they were already out of contention, any thoughts they might preserve their three-year unbeaten home record in Europe for the sake of pride alone was swept aside by Glasgow scoring six tries and galloping impressively into the last eight as pool runners-up to Munster.

It transformed the Tigers into a hangdog rabble of beaten and beleaguered figures long before the bitter end of a stunningly scoreless swansong in this season’s Champions Cup.

Glasgow ran in six tries at Welford Road (Getty Images)

The biggest gut-wrencher for Leicester is that while a series of heavy away defeats in recent seasons have been symptoms of a gradual fall from their former greatness, this was a new and painful feeling of the crisis being brought to their front door.

Leicester boos mingled with Glasgow followers’ chants of “We are Warriors” as Mathieu Raynal’s half-time whistle blew with the barely believable scoreline of Tigers 0 Glasgow 31.

Four first-half tries, all converted by the visitors’ fly-half Finn Russell, were begun in the sixth minute when Tommy Seymour cut a cute line to the posts after 27 phases of insistent, accurate attack.

Russell’s penalty pushed Glasgow out to 10-0 then Leicester’s full-back Mat Tait – a muted figure in a backline ravaged by injuries to Manu Tuilagi, JP Pieteresen, Matt Toomua, Owen Williams and Telusa Veainu – was harshly sent to the sin bin for a brushing block of Lee Jones’s run down the left wing. A penalty try soon followed when Leicester pulled down a line-out maul and the home side’s plight worsened as fly-half Freddie Burns missed two penalty shots at goal from medium to long range.

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Russell was relishing the front-foot ball supplied by the likes of Josh Strauss and Ryan Wilson at the breakdown, while the remarkable Jonny Gray showed up well in every facet of play.

Mark Bennett grabbed Glasgow’s third try with 29 minutes gone, on the end of passes from Strauss, Jones and Wilson, after some startlingly slick handling among the forwards. And Gray battered to the bonus-point try five minutes before the interval, as Ali Price and Jones snipped from a ruck deep in the Leicester 22.

It was up to Aaron Mauger, Geordan Murphy and the other Tigers coaches left in charge since the mid-season sacking of director of rugby Richard Cockerill at the start of this month to engender some kind of comeback.

But hooker Tom Youngs was left beating the turf in frustration after Wilson hurtled over for the fifth Glasgow try seven minutes into the second half, with Russell converting again for 38-0.

Records were already tumbling in fearful fashion for Leicester – their heaviest points total conceded in Europe was 41 away to Ulster in 2011-12; the biggest margin of defeat was 38-0 in Munster this season and the lowest European moment at home before this was a 32-10 loss to Leinster in 2000.

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Tim Swinson dotted down the sixth and final Glasgow try on 61 minutes after a carefree pass over the head by replacement scrum-half Henry Pyrgos.

As Glasgow’s all-international XV gloried in their history-making achievement, Leicester’s supporters must be asking many questions over the coaching set-up for the future, and how much can be put down to injuries in the last couple of years ruining the proper development of the first team.

Tigers are, it should be noted, still in the top half of the Premiership and they reached a European semi-final as recently as the World Cup-disrupted season of last year.

But the days of perennial Twickenham finals domestically appear out of reach in their current state of disarray.

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Two minutes before the end Leicester’s young England squad prop Ellis Genge was shown a yellow card for a blatant incursion into the side of a maul, and was seen discussing the matter with the referee after the final whistle.

The discussions over Leicester’s decline will go on much longer. This was the first time they had failed to score in a loss at home since they were beaten 35-0 by the Barbarians at Welford Road in 1969. Overall, it was their second-highest loss on this ground since the Baa-Baas won 73-19 here in 1998.

Man of the match Swinson said: “It’s a fantastic feeling, our goal was to get out of the pool and we’ve done it. We really took Leicester to the sword.”

Scorers:

Glasgow Warriors: tries: Seymour, penalty try, Bennett, Gray, Wilson, Swinson; conversions: Russell 5; penalty: Russell.

Leicester Tigers: M Tait; A Thompstone, P Betham (rep M Smith 65th min), J Roberts, T Brady; F Burns, B Youngs (S Harrison 50); G Bateman (E Genge 50), T Youngs (capt; H Thacker 63) D Cole (P Cilliers 67), E Slater, M Fitzgerald, M Williams (D Barrow 63), L McCaffrey (W Evans 75), L Hamilton.

Glasgow Warriors: S Hogg (P Murchie 70); T Seymour, M Bennett, A Dunbar (N Grigg 65), L Jones; F Russell, A Price (H Pyrgos 56); G Reid (A Allan 65), F Brown (P MacArthur 58), Z Fagerson (D Rae 65), T Swinson (B Alainu'uese 70), J Gray (capt), R Harley, R Wilson, J Strauss (C Fusaro 56).