Antonio Conte would not admit it after the match, but Chelsea’s progress to a second successive FA Cup final has been restorative. The Italian has worn a haggard expression on the touchline in recent weeks as his side’s pursuit of the top four was rendered ever more forlorn, his demeanour indicative of a campaign consumed by anticlimax. But the old zest and manic enthusiasm were back in plain sight at Wembley. Chelsea eased beyond Southampton to ensure a season that has served to underwhelm could yet yield major silverware.

The prospect of another spiky collision with José Mourinho, and Manchester United, in the domestic season finale will merely add to the sense of occasion. “There is not a problem between him and me,” offered Conte rather unconvincingly of a counterpart with whom he has sparred regularly during his time in England, with relations having reached a nadir this year.

“We are talking about two managers with strong characters and two winners,” he said. “And when in your mind, in your heart and in your blood there is the will to win … I have great respect for United’s story, for Mourinho’s story, and they have the same respect, I think, for Chelsea’s story and my story. But we want to win.”

The Italian’s career at Stamford Bridge is winding down prematurely, his departure anticipated in the summer but he can still go out with a bang. This was a semi-final claimed by his two strikers, Olivier Giroud supplying a goal of jaw-dropping quality in the opening exchange of the second half before the substitute Álvaro Morata added a late second, even if it was Eden Hazard’s effervescence which had most consistently illuminated the occasion.

The Belgian seemed to thrive playing in a competition that can still be won. Southampton, with Premier League survival their priority and four critical games still to be played, were aggrieved to have been denied a route back into the fray by the officials in the game’s frenetic latter stages. Yet in truth they rarely contained the irrepressible Hazard and had been badly unpicked by Giroud’s close control.

The Frenchman had scored twice against these opponents in the league just eight days previously but neither of those goals could match his opener on this grander stage. Cesc Fàbregas’s lofted pass forward 25 seconds into the second half had been optimistic but Hazard collected on the volley in mid-air ahead of Jan Bednarek and, once grounded, kept his head to flick the loose ball towards the penalty spot, where Giroud had evaded Mario Lemina in anticipation of a pass. The composure demonstrated thereafter by the Frenchman, in the tightest of spaces with markers flinging themselves in from all around, was startling.

A touch with his left foot took the ball away from Maya Yoshida, a second with his right cutting back to bypass Cédric Soares as he slid in. The slalom was played out at pace and, by the time the striker had calmly flicked home his finish with the outside of his right foot as he finally stumbled, Alex McCarthy and Bednarek had joined Soares in the pile of bodies cluttering up the goalmouth. “My second passion has always been skiing,” said the Frenchman, born in Alpine Chambéry whose first professional club was Grenoble, through a smile. Giroud’s control and subtlety of touch had been too much for Southampton. He has won all 10 of his club visits to Wembley, a record to which Chelsea will cling next month.

Mark Hughes’s side, who boast a solitary top-flight win since late November and languish four points below the relegation cut-off, had already survived Willian striking the crossbar by then with their initial display cramped by caution, but they did at least respond to their deficit. Shane Long’s dreadful first touch, after Wesley Hoedt’s diagonal pass and Charlie Austin’s dummy, passed up a fine chance to equalise. The introduction of Nathan Redmond and Dusan Tadic injected “craft”, according to Hughes, though luck remained elusive.

Willy Caballero, initially wrong-footed, had done wonderfully well to improvise a save and deflect Redmond’s shot from distance behind with his left arm as he fell. Yet the goalkeeper was far less convincing from the resultant corner, leaping to catch a high ball under pressure from Austin only to spill back, behind and over his line. His blushes were spared by the referee blowing for what seemed a soft foul. “The keeper’s basically thrown the ball into the back of his net, and if ever there was a situation for the VAR to step in, that was an opportunity,” Hughes said. “It was a match-defining moment. Why it wasn’t referred, I have no idea.”

He also bemoaned the non-award of a penalty after the ball struck Giroud’s arm and saw Austin skim a shot on to the far post before the end. Yet by then Chelsea’s lead had been doubled. Morata had been on the pitch only a few minutes when César Azpilicueta gathered in space and flung over the kind of cross from which successive Chelsea forwards have prospered in recent times. His compatriot had eased far too comfortably away from Hoedt and his downward header bounced beyond the helpless McCarthy.

“In this type of game, the most important thing is to reach your target,” Conte said. “To reach another final is very important for the players, important for the club, and especially it is important for the fans. I’m delighted for them.”

It may not be enough to prolong his stay into a third season but Conte can still emerge from a trying campaign with a trophy.