Those supporters who succumbed to the heady combination of heat and Keo, the local brew, missed a treat. The game might have started late, but the outcome was wrapped up inside half an hour. Scotland were rampant.

The Larnaca Lions won’t enter the Scottish lexicon in the way those of Lisbon have. And overcoming opposition as moderate as Cyprus does not deserve veneration. But this was another night to savour. We ought not dismiss this victory, particularly given what now seems incontrovertible: Scotland are heading to Germany next summer and a second successive European Championships.

Ranked 118 in the world, and seemingly spurned by their own fans, just a few hundred of whom turned up for this, Cyprus are far from giants of world football. Nevertheless, this was still mightily impressive from Scotland The outstanding Scott McTominay got the ball rolling just four minutes in with his sixth goal in his last five international outings. The more unlikely figure of Ryan Porteous made it two after 16 minutes and then John McGinn did what he does when curling a shot inside the far post from just inside the box. McTominay later hit the post with a curled effort that denied the prolific midfielder another brace.

Scott McTominay heads home Scotland's opening goal in Larnaca against Cyprus.

Scotland continue to sail in uncharted territory. The win over Georgia earlier this summer was the first time Scotland had begun a qualifying group with four straight victories. Well, add a fifth for good measure. And who knows, maybe a sixth might come next time out in Seville. It may not even matter by then. Should Norway draw with Georgia in Oslo on Tuesday night, when Scotland are taking on England in an anniversary friendly, then there will be a party to end all parties. Even Clarke might crack a smile.

Typically, he stayed out of the way as the team applauded the fans at the end. He did make a point of shaking the hand of each player as they left the pitch, reserving a big bear hug for Porteous, who as well as scoring his first international goal, made a goal-saving challenge on substitute Ioannis Pittas near the end.

All in all, it was another masterclass from Clarke. He has built a proper team. Choruses of “There’s only one Steve Clarke!” were being sung from the banks of the AEK Arena long before half time as Scotland threatened to run amok. McGinn even tried to shoot from his own half on one occasion. Around 16 yards or so is more his distance, and he finished in familiar style to put the visitors three up after 29 minutes. For a spell, it looked as if Scotland might be trying to match Spain’s tally against Georgia earlier in the evening by hitting seven on the road. In the end, they had to be content with just three. Of more significance are the three points.

All the pre-match confidence, which spooked many longer-standing Scotland watchers, was well-founded it turned out. But amid all the innovation, the set-piece specialists and the sports scientists who ensured the players were sufficiently hydrated in the muggy conditions, it was gratifying to note something as simple and as old school as a quickly taken throw-in was what set Scotland on their way. Che Adams spotted Andy Robertson’s dash down the left and swiftly launched the ball into his path. Only moments earlier the Liverpool full back had sent a poor cross behind after McTominay had made a dangerous run to the back post but he made up for it on this occasion, and the Manchester United player profited. It did require a flick on from McGinn with McTominay stretching every sinew to head in ahead of Andreas Karo.

Ryan Porteous scored his first goal for Scotland as they cruised to victory against the Cypriots.

McTominay was running the show in the early stages. Anderson Correia was booked for a crude foul as the midfielder strode in field from the right, where he was proving unplayable. Scotland’s physical dominance was telling, with the strapping McTominay to the fore. Not that the visitors were having it all their own way, however. A couple of passages of play provided jolts. A quick break led to Pieros Sotiriou hitting the bar, but a teammate had strayed offside. Grigoris Kastanos then thumped a shot just past Angus Gunn’s left post.

A second goal was therefore supremely welcome for the visitors and it was a set-piece straight out of assistant coach Austin MacPhee’s book. Robertson’s deep free-kick from the left was headed down by Jack Hendry, and Porteous took a touch before lashing the ball into the net. The Scotland fans who made up around three-quarters of the crowd of over 7,000 were rubbing their eyes. This wasn’t normal. And better was to come when McGinn made sure of the outcome after he was picked out by McTominay. More goals should probably have followed. Adams seemed to pull out of going for a delicious Robertson cross while Callum McGregor shot too straight at Joel Mall. Another cross from the excellent Robertson flashed across the face of the goal. McTominay was unlucky to see a shot hit Mall’s far post and come back out.

The cries of Ole! had begun by the 65-minute mark. Goalkeeper Gunn had already been asked for a wave by fans who were by now revelling in the novelty of a comfortable away victory. Clarke had the luxury of making changes with the little matter of a game against England in mind. Kenny McLean and Lyndon Dykes were handed valuable minutes, so too Stuart Armstrong, Nathan Patterson and Ryan Christie. Scotland’s next three games will see a steep increase in quality of opposition: England, Spain and France. They might still need a point to qualify in Seville next month. Who would bet against them getting it?

Scotland continue to sail in uncharted territory: Euro 2024 now so close after Cyprus, fans succumb to heat and Keo, a proper team has emerged