Italy’s manager, Milena Bertolini, was asked how she intended to celebrate her 53rd birthday on Monday. “We want to move forward from the round of 16,” she answered without hesitation. “This would be the most wonderful birthday present. We have worked so long and hard to achieve this result.”

Her players belatedly delivered 24 hours later, sending Le Azzurre into the World Cup quarter-finals for the first time since 1991 with a composed two-goal victory over China in Montpellier. Making their tournament return in France after two decades in the footballing wilderness, Bertolini’s side are now only three wins away from lifting the World Cup.

Italy v China: Women's World Cup 2019 last 16 – as it happened Read more

“It is a great gift,” the coach joked afterwards. “I don’t know how far we can go in the tournament. We are giving absolutely everything in every match – but we know that the further we go in the competition, the higher the level will become.”

Following rousing renditions of their respective national anthems under the burning Mediterranean sun, both teams began cautiously – as if needing a moment to catch their collective breath.

Juventus’s Cristiana Girelli created the first opportunity in the 11th minute, slicing open China’s defence with a spectacular turn-and-pass towards Valentina Giacinti. The 25-year-old appeared to have opened her World Cup account with a driving shot past Peng Shimeng only to be called back for offside.

Giacinti, making her second start of the tournament, did not have to wait long to compensate for that mistimed run. A darting move down the right-hand flank minutes later left the Milan forward alone and in possession. She crossed the ball, before – following a scramble in the penalty area – she collected a deflection from Peng’s attempted charge-down and converted to put Italy in front.

Giacinti should have doubled her tally in the first half, finding herself one-on-one with Peng only to shoot wide – and then again receive another offside call. Such infractions have been a persistent theme of Italy’s campaign; they had two goals disallowed against Australia in the opening group match and another chalked off against Brazil last week. It has not hurt them – yet.

China wrestled back momentum in the latter stages of the first half, almost equalising on several occasions. But the interval halted the Iron Roses’ momentum, and Italy soon regained control.

Five minutes after the resumption their first-half substitute, Aurora Galli, effortlessly dispatched the ball from the edge of the penalty area. As it flew into the bottom left corner past a diving Peng, it was clear to the ecstatic Italian fans that a hitherto nervy encounter had virtually been won. Try as they might, China were unable to conjure a reply – let alone two – as the half moved towards its conclusion.

Italy now return to Valenciennes for Saturday’s quarter-final, their third game in the northern city, against the Netherlands. China, meanwhile, have plenty of soul-searching to undertake on their long journey home. Once a women’s footballing powerhouse and a two-time World Cup host, they have departed the tournament before the quarter-finals for the first-time.

Before Tuesday’s game, Italy’s captain, Sara Gama, was asked if her teammates were suffering from vertigo after unexpectedly topping group C . In Montpellier on Tuesday, her team’s clinical victory indicated they do not seem to be afraid of heights.