Thirty-one points adrift going into Friday’s second leg, they will need far greater incisiveness, not to mention a thick slice of luck, if they are to go through to a meeting with Newcastle Falcons or Montferrand.

Saracens may be bumping along close to the bottom of the Zurich Premiership, but when Thomas Castaignede is on song they can be a threat to anyone.

The Frenchman, apart from the odd wayward place kick, was just about pitch perfect in this second-round tie: he may be out of favour with his national selectors, but on this form he is still one of the most entertaining performers in European rugby.

The Frenchman contributed two converted tries and three penalties before taking his leave with ten minutes to go, the other touchdowns coming from Kyran Bracken, substitute Robbie Russell and his namesake Ben Russell.

Two penalties from Dan Parks were the only counters for a Glasgow side who muscled their way back into the game in the second half but were unable to get even the single try which might have given them a glimmer of hope.

Hugh Campbell, who had aimed to stifle Saracens in the first leg, did not concede that the tie was over and suggested that the return leg could be an entertaining affair. "With that sort of lead Saracens would be entitled to think they’ve done enough, but I think they will write off Glasgow at their peril," said the Scottish side’s coach.

"It should be a real cracker at Hughenden on Friday. We have to go out and score points, and obviously they have the ability to counter-attack from anywhere on the pitch."

True to the form book in such situations, the Saracens coach, Rod Kafer, also insisted the tie was not a foregone conclusion, and put the margin of his side’s victory down to good fortune.

"The clear problem for us now is thinking it’s over and becoming complacent. We were lucky today at times, and I feel for the Glasgow guys as there have been games this season when the breaks went against us."

Saracens, though currently without the injured England flanker Richard Hill, can still boast a more than useful pack, and it was those forwards who ensured them of a massive territorial advantage in the early stages.

Captain Simon Raiwalui led by example with some bludgeoning runs, while when the ball did go out to the backs, the pacy Paul Bailey always looked dangerous.

The English side should have taken the lead in the ninth minute, but Castaignede was off target with a very kickable penalty. It took just six minutes though for the French stand-off to make amends.

Awarded a penalty out on their left, Saracens opted to kick for touch. Castaignede did the honours, and then from the resultant lineout skipped effortlessly past Parks to score beneath the posts and make his own conversion a formality.

A couple of minutes later an offence in the tackle by Raiwalui allowed Parks to get Glasgow on to the scoreboard, but by the half-hour mark two further penalties from Castaignede had stretched Saracens’ lead to 13-3. To make matters worse for the visitors, their captain, Cameron Mather, was sinbinned for a high tackle on Bailey.

Campbell later called that a crucial moment, and, although Saracens’ superiority was already apparent, the loss of a key forward did no favours to Glasgow, who conceded ten more points in their skipper’s absence.

As the rain continued to fall and the pitch began to cut up, the visitors were in danger of being swamped. Five minutes from the interval, their seven-man scrum withstood two attempts at a pushover try, but when they were awarded the put-in for the third set-piece they failed to secure possession.

Instead, Saracens took the scrum against the head, and scrum-half Bracken darted round the blindside for his team’s second try.

Castaignede converted that one, then five minutes before the break did further damage with a superb individual score, taking a couple of hacks at a loose ball, then a more controlled dink from within the Glasgow 22, and finally just getting the touchdown before the dead-ball line was crossed. Again, however, he missed the conversion, and with the last kick of the half Parks’ second penalty made the score 25-6.

As Mr Berdos blew his whistle, Robbie Russell was standing on the touchline waiting to come on for Raphael Ibanez. His introduction delayed by the break, the Scotland hooker wasted little time in making an impact when he was allowed on, collecting the first score of the second half with a clear run from halfway after Glasgow had been dispossessed in the tackle. The conversion made it 32-6.

Glasgow then enjoyed their most sustained period of pressure in the game, and should have made the most of it when the yellow-carding of Raiwalui for persistent offending gave them a numerical advantage.

But even when they did succeed in retaining possession through a number of phases, they were often doing so on the back foot.

Just as the match itself looked like doing so, an increasingly cavalier Saracens broke upfield, and Ben Russell was on the end of a move down the right to complete the scoring.

Report from Stuart Bathgate of The Scotsman.