Ange Postecoglou had talked about how keenly Tottenham felt their absence from European competition last season – a “real gap in our calendar”, as the manager put it. And so what was a further 35-minute wait?

It was a night of transport chaos around the stadium, overland trains suspended, roads blocked and kick-off delayed. It set the tone for a wild tie against Qarabag, Tottenham’s Europa League curtain-raiser featuring a red card for their centre-back Radu Dragusin inside seven minutes and countless close shaves in front of their goal. How did they manage a clean sheet? Guglielmo Vicario was a big part of the reason.

Related: Tottenham 3-0 Qarabag: Europa League – live reaction

Spurs made their punches count at the other end and when Dominic Solanke made it 3-0 in the 68th minute, they could coast to victory. Which is not a line that chimed with much of what had gone before.

Brennan Johnson, though, made it three goals in three games with the opener and Pape Sarr got the second, leaving the club’s fans to revel in a fun occasion. It will be a long road to the final in Bilbao. Spurs are up and running.

The Qarabag bus had been caught in the grinding traffic, having wended its way from the team hotel in Stratford – a mere 12 miles away, hardly the Baku beyond. The Azerbaijan champions only arrived inside the stadium at 7.45pm, far from ideal for them. Or Spurs.

“Imagine you are caught in traffic for more than two and a half hours,” said Gurban Gurbanov, the Qarabag manager. “There were no police to escort us and when we arrived, we were told in 40 minutes we had to start. Obviously it had a big impact on us.”

There were early errors on both sides, huge ones, starting with Dragusin’s sending-off after he inexplicably allowed the ball to run away from him as the last man with Juninho applying the pressure. Dragusin was in trouble when he was robbed by the Qarabag striker, who threatened to run clear on goal. When Dragusin pulled at Juninho’s shorts, the referee, Willy Delajod, knew what he had to do.

Tottenham were undaunted. Postecoglou got Destiny Udogie on at left-back (the unfortunate Lucas Bergvall withdrawn from midfield) to reform the back four, albeit one that was never going to play as such. It is not Postecoglou’s style. Archie Gray continued to push up from right-back. Udogie did the same. Ben Davies ran upfield with the ball at his feet from his new position of left centre-back.

It said plenty about Spurs that they had carried on playing with nine men for what seemed like an age after Dragusin’s dismissal and as Udogie warmed up. They did not put the ball out. They would even lose it at one stage, playing with fire. Tottenham would do plenty of that, the examples numerous.

Spurs’s breakthrough came immediately after the Udogie for Bergvall change and it was a personal disaster for the Qarabag defensive midfielder, Júlio Romão. Spurs brought an aggressive press and Ramão turned into Solanke, who advanced before playing in Johnson on the overlap. The first-time finish was low and true.

Johnson might have scored again when he got onto a long ball from Gray and evaded the goalkeeper, Mateusz Kochalski, who had made a rash bolt from his line. Johnson rolled wide of the empty net. But the remainder of the first half was a story of Spurs taking risks at the back and getting away with them, leaving themselves with men down against the Qarabag counter, backing themselves to recover.

Toral Bayramov air-kicked under pressure from Udogie after surging through and nobody could understand how Juninho rolled wide of the far post from an Elvin Jafarguliyev cross when unmarked in front of goal. Patrick Andrade shot wildly when well placed and there was also the moment when Juninho robbed Davies and Spurs needed Vicario to leave his line and make a saving one-on-one tackle.

Postecoglou introduced Dejan Kulusevski for Johnson at half-time and it was the Sweden winger whose inswinging corner set in motion the second goal. Kochalski came and flapped under minimal pressure – he was impeded more by one of his own players – and Sarr fashioned a sweet connection on the volley, too sweet for Andrade on the line.

Spurs were in no mood to make things straightforward. Was it not an idea for them to defend properly? Yves Bissouma conceded a penalty with a clumsy challenge on Jafarguliyev only for Bayramov to blaze high and Qarabag had a fistful of further chances, mainly after forcing turnovers. Their finishing was dismal.

Spurs did not feel safe at 2-0 but Solanke, who had been denied by Kochalski on 58 minutes, enabled them to breathe more easily. Not for the first time, Kochalski wobbled, patting a Son Heung-min shot straight to Solanke. It was a tap-in for the striker.

Jafarguliyev saw Vicario tip away his top corner-bound blast and when Juninho finally had the ball in the net, the offside flag obviously had to go up. Qarabag could have played all night and not scored.