Normal service has been resumed. Chelsea emphatically checked the recent hint of a stagger and rediscovered the relentless, ruthless form which will surely earn them the Premier League title. Southampton may have been slippery opponents but they were overcome to re-establish a seven-point advantage at the top and steel the leaders for the run-in. The pressure has been thrust back on their closest pursuer. Over to you, Tottenham Hotspur.

Antonio Conte had worn a scowl for much of this match, pounding his technical area as furiously as ever and kicking everything from water bottles to medical bags whenever his players’ concentration lapsed. “I wanted to kick the ball because sometimes, believe me, I want to play,” said the Chelsea manager in the aftermath as the adrenaline gave way to exhaustion. “But I know that if I kick the ball, the referee will probably send me off.”

And yet, by the end, he was pointing to the heavens in delight as Diego Costa, a beast awakened, scored twice after the interval to nullify the visitors’ threat and banish memories of that recent 2-0 defeat at Manchester United.

Antonio Conte praises ‘psychological step’ in Chelsea’s title push Read more

The Italian acknowledged just how significant this victory could prove to be, potentially sapping hope from Tottenham’s before their tricky trip to Crystal Palace on Wednesday night. “It feels like a massive step,” said Gary Cahill, whose thumping header had restored the home side’s lead in first-half stoppage time. Costa may have caught the eye with his first league goals since early March, but it was the captain’s timely effort which set the tone. His was the kind of goal John Terry might once have supplied.

Play Video 1:15 Chelsea's win over Southampton 'a big psychological step' towards league title, says Conte – video

Plenty of Chelsea’s key performers had risen to this occasion before the end. Cesc Fàbregas was outstanding, striking delicious passes from deep when he was not trading challenges with Oriol Romeu. The cross he arced over from Eden Hazard’s short corner nine minutes into the second period proved to be his 103rd Premier League assist, with Costa holding off Ryan Bertrand to plant a header into the net. Hazard was a livewire, maintaining the high standards he has set all season. Southampton had been guilty of losing him early on as he ambled on to Costa’s lay-off, eluding Romeu in the process, to fire an accurate finish across Fraser Forster and into the corner.

Then there was Costa, such a frustrated presence over recent weeks, rediscovering his touch after five scoreless performances in the league. His second goal seemed like a release, the passes snapped swiftly between the forward and Hazard, then Pedro, before he wrong-footed Fraser Forster and slid in the fourth. Conte has always pointed to the forward’s selfless contribution, running the channels and unsettling defenders, but he needed proper reward for those efforts. Should he depart for China in the summer he would be going into his last month with Chelsea bolstered. A title would be a fitting way to go out.

Chelsea needed this after Old Trafford. There had still been periods when Southampton’s players, fresh from a weekend off, had threatened to wrest the initiative but just as at Wembley in the FA Cup semi-final against Tottenham, the more clinical team would prevail. The visitors were at their most troublesome when Soufiane Bufal and Dusan Tadic were scuttling down the wings, fed by the busy energy and canny deliveries of Steven Davis and James Ward-Prowse.

The England midfielder had delivered the corner from which Chelsea conceded, for the 11th Premier League game in succession, before the half-hour mark. Nemanja Matic’s inadvertent flick had set the home defenders on their heels, with Manolo Gabbiadini allowed time to collect and turn inside before poking the loose ball back across goal. Thibaut Courtois’ touch presented it to Romeu and the former Chelsea player simply could not miss.

There was a period thereafter when Chelsea threatened to wilt, but a barnstorming run down the right from N’Golo Kante seemed to shake them awake once again, with Cahill’s telling contribution delivered shortly afterwards. The centre-half had spent two nights in hospital last week recovering from a severe bout of gastroenteritis, and missed Saturday’s semi-final. “The lads didn’t miss me at Wembley,” he said. They needed him here, easing away from Cédric Soares as Southampton’s back-line laboured to repel crosses from either flank in quick succession. Marcos Alonso looped a header back towards the six-yard box where Cahill powered his attempt down and in. He had actually risked an immediate return to casualty by taking the header clean off Costa’s boot as the striker attempted an overhead kick.

Chelsea did not look back and even offered Terry his first taste of Premier League football since November in what time remained, with Bertrand’s late goal for the visitors a mere consolation.

Conte’s side now need four victories from their remaining fixtures to become champions, although that is supposing Tottenham maintain winning form during their trickier run-in. Spurs have no leeway and the leaders will watch events at Selhurst Park on Wednesday with interest, but they can sense the title edging ever closer. “We must be confident about the future,” added Conte. “We only have to think about ourselves.”