The Netherlands got the job done at Bramall Lane in sweltering conditions to secure progress to the quarter-finals but despite a 4-1 win they did not score enough to top the group and will next play a dangerous-looking France.

The Netherlands needed a draw to qualify and were level until three late goals, two from the substitute Romée Leuchter, secured victory.

The holders were tested early on by Switzerland’s persistent, high press. Such was the effectiveness of Nils Nielsen’s 4-2-3-1 that Switzerland was able to deny Lieke Martens, usually a defensive nightmare on the Netherlands’ left flank, access to the ball.

In contrast, Switzerland’s attack was powering through the opposition midfield with ease, evident through Sandy Maendly’s curling effort in the 12th minute that had to be tipped over by Daphne van Domselaar and highlighted also by Ramona Bachmann’s swashbuckling runs down both flanks.

A sloppy start from the Netherlands buoyed Switzerland’s qualification hopes. But what Switzerland had failed to factor in was the Netherlands’ second wind – which they have displayed in all their performances across the Euros.

As the Netherlands’ attack regained more possession, more passes got through to Martens and Lineth Beerensteyn. In the 20th minute Beerensteyn latched on to one of those through balls. Driving towards Gaëlle Thalmann’s goal, her long legs seemed to become entangled with the keeper’s hesitant hands and the referee, Juliana Demetrescu, pointed to the penalty spot.

A few moments of VAR inspection later and replays would show the keeper had just got a glove to the ball. The overturned decision, however, allowed only a brief reprieve before Mark Parsons’ side got going again.

First, Jackie Groenen unleashed a volley from close range from a smart set-play routine. Next, in the 34th minute, Martens’ looping header was pushed over by Thalmann’s outstretched fingers.

Nielsen’s team would have to summon the same energy after the interval that they had started the game with to create a shift in momentum. However, before they could muster a charge, Ana-Maria Crnogorcevic had headed into her own goal.

The Swiss had been attempting to clear Stefanie van der Grat’s header from a corner. Instead, she gave her side the mountainous task of needing to score twice. Yet where there’s a will there’s a way, chiefly in Bachmann. The attacker muscled her way into the box four minutes later, squaring to Géraldine Reuteler who toe-poked past Van Domselaar.

Van Domselaar would be in the thick of the action shortly after when she made three saves to keep her side level while the Dutch defense faltered and tottered.

Parsons’ response would be controversially take off the experienced attackers Martens and Beerenstyne, along with the steadfast defenders Aniek Nouwen and Jill Roord. Perhaps he had one eye on Saturday’s quarter-final and a focus on helping his star players through 30-degree heat.

The mass exodus did not matter. The Netherlands continued their assault on Thalmann’s goal and the Swiss keeper had to make a brilliant array of saves to keep it 1-1. It took a decisive Leuchter header from Lynn Wilms’ cross for her goal to be breached again, before the floodgates for the third and the fourth during stoppage time.

Parsons said: “The match against Switzerland was a wild game, a rollercoaster. Conceding after half-time is always tough, but we found our legs again and got the game under control.”

Victoria Pelova got the Netherlands’ third goal from close range and her attempt at another shot set up Leuchter to complete the scoring.

Nielsen acknowledged his side’s defending had been lacklustre in the final moments and said: “It was always going to be a tough game against the Netherlands; they are tournament favorites and we weren’t sharp when needed to be.”