In a cacophony of jubilant celebration, the sense of relief inside Stamford Bridge was overwhelming.

Just as Chelsea feared their Champions League dreams fading away, Marc Cucurella nodded the biggest goal of their season and a firecracker in west London ignited. So infectious was the joy that one home supporter even charged on to the pitch before the match was done. Call his solo pitch invasion passion or stupidity; it was just that kind of feeling.

For 71 minutes Chelsea had toiled, struggling to find a way past a dismal Manchester United team that have now not won in the Premier League for eight matches. But then came salvation: a sumptuous Reece James pirouette, his beautiful dinked ball to the far post and a powerful header from the floppy-haired Spaniard. Who needs effective attackers when full-backs can provide such delightful goods?

With only a visit to Nottingham Forest remaining, Chelsea are guaranteed to occupy a Champions League spot heading into the final day. The battle for Europe’s premier competition is going to the wire.

“The win was very important,” said Enzo Maresca. “I think tonight we struggled on the ball because we didn’t expect them to be so aggressive man to man. They surprised us a little bit with that. But we created enough chances to win. From the first to the second half, we deserved to win the game.”

So, the overriding positive: Chelsea’s top-five fate remains in their hands with this victory matching that of an Aston Villa team who beat Spurs but have a far inferior goal difference.

The concern for a season-defining final-day fixture at the City Ground was the almost entire absence of attacking spark on display.

Shorn of the suspended Nicolas Jackson for the remainder of the campaign, nor with any senior back-up striker fit and ready for action, Maresca was forced to hand a first Premier League start to Tyrique George. Leading the line, the 19-year-old managed just 14 touches all match, failing to generate even a sniff of the United goal, although Maresca insisted he was pleased with George’s performance.

The closest the teenager came, on the hour, was when tumbling to the ground under the force of the onrushing André Onana, prompting Chris Kavanagh to point to the spot. Onana was aghast, the referee was sent to the screen and justice prevailed when replays showed a clear goalkeeper glove on the ball.

For all that they dictated vast swathes of the game, the hosts rarely prompted any elevation in Onana’s heart rate, Cole Palmer and Noni Madueke desperately endeavouring – but not managing – to create amid a worrying absence of potency in front of goal. That Madueke failed to double Chelsea’s lead, driving wide when sent clean through with only Onana to beat, spoke volumes.

Thankfully Chelsea could call upon their full-backs. James’s pinpoint cross for the goal came without so much as a glance up to check where the delivery was required, while Cucurella’s header was unstoppable.

In fact, James had earlier come closest of all the Chelsea players to scoring in the first half when he cut across a bouncing ball from range, fizzing the sweetest of strikes with the outside of his boot against a United upright. “The Champions League is where the club belongs,” he said. “Competing in the best competitions. People like to write us off and call us young, but it’s an experienced Manchester United team and we did what we needed to do.”

So what of United? An 18th league defeat of the season is their worst tally since 1973-74, and they managed just one shot on target all match.

That statistic does not include the solitary time they did have the ball in the Chelsea net 16 minutes in. The game was goalless at that point when Harry Maguire, displaying his newly developed penchant for masquerading as a centre-forward, expertly turned Bruno Fernandes’s inswinging cross goalwards. Replays showed his shoulder was a couple of inches offside as the ball was delivered.

Of course, United’s dreadful season rendered this match little more than a sideshow for them before Wednesday’s Europa League final with Tottenham. Unlike Ange Postecoglou – who fielded an almost entirely second-string Spurs side in the defeat at Villa – Ruben Amorim risked naming perhaps the strongest XI at his disposal here in a change of tack from the defeat by West Ham last time out.

“If I put some players out it would be 10 days without a game,” he explained. “I don’t like that. I think the best way to prepare for the final is just to compete. We are Manchester United so we need to compete in every game.”

They barely did here, but his players all departed Stamford Bridge with a clean bill of health, which is of far greater importance for now. Everything hinges on Wednesday.