There have been plenty of occasions this season when Chelsea have appeared broken beyond repair. Their title defence fizzled out early but points had been frittered away before the onset of spring as the campaign degenerated into an apparently hopeless pursuit of Champions League qualification. But in the final week they have given themselves a chance and are on the top four’s shoulder once again.

By defeating third-placed Liverpool here courtesy of Olivier Giroud’s first‑half goal, a header guided into the corner as the visitors switched off for Victor Moses’s cross, their chase is prolonged. All Antonio Conte and his players can do is ensure Huddersfield and Newcastle are beaten in the last five days and then pray , somehow, Tottenham Hotspur or the Champions League finalists slip up in their own appealing home fixtures.

Success remains a long shot but, as Conte admitted, Chelsea would have considered such a target “impossible” only a month ago. Four wins on the trot have fired hope.

The late rally is tinged with regret. Those horribly damaging defeats to Bournemouth and Watford spring to mind when reflecting on a turbulent season, but so might the flurry of draws at the turn of the year or, even, the wasteful 1-1 draw with West Ham only a month ago. When they lost at home to Spurs at the beginning of April, the chasm to fourth had gaped at eight points. “Now we are getting three points in every game and our opponents are dropping points,” Conte said. “Our future is not in our hands but we have to try to put pressure on the teams ahead of us.”

Giroud’s goal, cushioned into the corner as he leapt between Virgil van Dijk and Dejan Lovren, and some feverish defending, secured this latest win. Thibaut Courtois was authoritative and imposing. Gary Cahill, rejuvenated over recent weeks, relished the scrap of it all with César Azpilicueta and the excellent Antonio Rüdiger flinging themselves into blocks and challenges at his side.

Rüdiger had played with Mohamed Salah at Roma and was instrumental in blunting the footballer of the year. The Egyptian’s frustration saw him booked for a dive over Cahill’s first‑half tackle. For once, he actually seemed rattled.

Sadio Mané, in particular, and the substitute Dominic Solanke still threatened to restore parity, but Chelsea would not be breached. Their former academy player twice nodded over the bar near the end, straining but failing to keep his headers down. His time will come. “He’s a hard-working boy,” said Jürgen Klopp, who had clearly sensed the potential theatre of flinging the 20-year-old into the fray against his former club. “He will be fine in the future.”

Klopp will be irritated his team’s final domestic game, against Brighton, may no longer be irrelevant given he would have preferred to rest personnel before the European Cup final in Kiev. Liverpool had required a result on the final day of last season, in a home game against relegated Middlesbrough, to qualify and may now have to repeat that trick.

“That’s my life, always going to the last day,” Klopp said. “But I saw Brighton against Manchester United on Friday and they don’t look like an easy game. They were really good that day. But it’s football. If you want guarantees, do something different. The boys have shown me they will try and try and try.”

His players certainly did not seem spent after their exertions in Rome in midweek and monopolised the ball for long periods, though they ran aground too often on the clutter in Chelsea’s penalty area. It only took them being marginally off their effervescent best to offer the home side their chance.

Even Tiémoué Bakayoko, much maligned over his first season in this country, seemed to revel in the rearguard action, with the hosts’ counterattacks always carrying a considerable threat of their own. Eden Hazard, his shirt ripped and replaced, led the charge and was irrepressible until replaced by Willian late on.

Giroud, so impressive since arriving from Arsenal in January, offered a focal point to exploit. No one can match the 29 headed goals he has scored since arriving in London from Montpellier almost six years ago. He has given his team hope once more.