For England, it was always going to be about finding the moment, the one to blow apart a tight game, to cut through so much negative tournament history – particularly at the hands of Germany. And for long spells, as the tension rose to near unbearable levels at a raucous and emotional Wembley, the home crowd wondered whether it would come.

Gareth Southgate had reverted to a 3-4-3, ignoring the clamour for greater fantasy and more creative players. It was the England manager sticking bravely to his principles, seeking security, the platform for the moment, and a part of the equation was patience, which was not in abundant supply inside the stadium.

Related: England 2-0 Germany: Euro 2020 player ratings from Wembley

Germany had shown their quality in the first half, particularly early on, yet England came to match them physically and tactically. The longer the second half wore on, the greater the assurance of those in white shirts. Could they find the incision, the note of clarity?

Southgate had called for a hero, somebody to score a goal that will live for ever, and with 15 minutes to go he found one. Yet again, it was Raheem Sterling. After his match-winners in the group stage against Croatia and the Czech Republic, Sterling bristled with confidence and hard running. The qualities were stamped all over the goal that ignited English dreams.

Southgate had introduced Jack Grealish from the bench and the midfielder was involved in the move, taking a pass from Harry Kane and ushering in the overlapping Luke Shaw on the left. But it was Sterling who started the move and it was he who finished it, driving into the box to guide home Shaw’s low delivery. Sterling has scored 15 times in his past 20 England appearances.

The abiding image of the occasion from a German point of view would come shortly after. It was of Thomas Müller, his face contorted in despair. It was always going to be about moments and Germany’s came on 81 minutes when the veteran was sent clean through by Kai Havertz.

A few minutes earlier, Müller had blasted a free-kick into the wall from the edge of the area. Now he had to find the equaliser. Wembley fretted. Yet the finish was dragged low past Jordan Pickford’s right post. There was relief for Sterling, who had left a back-pass short for John Stones, sparking the opening.

England sensed only their second knockout phase victory at a European Championship – the first had been against Spain on penalties in 1996 – and also an end to the crushing sequence of German dominance over them. Germany had won the past four meetings in the knockout rounds of major finals.

It fell to Kane to make sure and, after his struggles in front of goal, it felt impossibly sweet for him and everybody with England in their hearts when he stooped to nod home a Grealish cross. It had followed another thrust by Shaw and was the prompt for the mother and father of all parties to break out in the stands.

For Southgate, there was personal atonement for his infamous penalty miss here against Germany in the Euro 96 semi-final but, more broadly, the sense that England had located the ignition key. The hard truth is the nation is not noted for an ability to beat established teams in the knockout rounds of major finals. Since the World Cup triumph of 1966, the only serious scalp has been that of Spain.

Now the sense of possibility cannot be ignored, particularly with the draw to the final having opened up. Pickford has come to radiate assurance behind a miserly defence and the statistics show it is four clean sheets out of four; the last time that happened for England at a tournament, Bobby Moore ended up lifting the Jules Rimet trophy.

Related: England 2-0 Germany: Euro 2020, last 16 – live!

Southgate’s players had to suffer, with Germany subjecting them to a harrowing opening 10 minutes, pressing high and running at the England backline. Rice was booked for a foul – Havertz wasted the free-kick on the edge of the area – but how the young midfielder managed the game thereafter. Alongside Kalvin Phillips, he was excellent. They were not alone.

England dug out a foothold, with Bukayo Saka showing a couple of flashes on the right, even if there was the worry in the first half about whether they could retain possession or show the needed precision with it.

Sterling extended Manuel Neuer with a shot from distance on 16 minutes and Harry Maguire headed high from a Kieran Trippier cross. Kane fed off scraps – again – although he almost found one in first-half stoppage time. Sterling burst into the area and, when the ball broke kindly for the captain, he looked favoured to score. Mats Hummels nicked the ball away from him.

• Download the Guardian app from the iOS App Store on iPhones or the Google Play store on Android phones by searching for 'The Guardian'.

• If you already have the Guardian app, make sure you’re on the most recent version.

• In the Guardian app, tap the yellow button at the bottom right, then go to Settings (the gear icon), then Notifications.

• Turn on sport notifications.

Germany had regrets before the interval, the biggest coming after Havertz released Timo Werner. The angle was tight but Werner still had plenty of goal at which to aim. Pickford made a vital block. The goalkeeper would continue to excel after the interval, tipping over a Havertz rocket.

Southgate had wanted to mirror Germany’s formation, to contain the threat of Joshua Kimmich and Robin Gosens in the wing-back positions, which was achieved. And he got the timing of Grealish’s introduction just right. Grealish contributed fully, although not as much as the irrepressible Sterling. England have glory in their sights.