There were periods here when Antonio Conte must have feared recent history was repeating itself. His Chelsea side had huffed and puffed their way through the opening period, their shot tally mounting without success (for all that their efforts were occasionally rather wild), with Brighton & Hove Albion holding firm until concentration lapsed in the opening 40 seconds after the break.

The champions would eventually win in comfort to paper over some of the cracks but a half century of shots in the fixtures either side of Christmas have yielded only two goals.

The Italian was rather stating the obvious with his post-match assessment that “if we learn to be more clinical, and to try to exploit the many chances we have during games, it will be better for us”. Álvaro Morata now has 10 goals, six assisted by César Azpilicueta, to show for his first Premier League campaign, and yet it is still tempting to wonder whether Diego Costa’s brute strength or ability to unnerve his markers, whether legitimately or not, is still being missed.

Certainly while this contest drifted Chelsea were far too reliant upon Eden Hazard for inspiration, with the Belgian retreating ever deeper to collect the ball. He was only properly liberated once the hosts were ahead.

Conte will use his team’s initial toils here, as well as at Goodison Park on Saturday, as evidence that reinforcements are required next month: another forward to ease the burden on both Morata and Hazard, a forward-thinking wing-back to challenge Marcos Alonso down the left and, if the budgets stretch far enough, maybe a central creator.

Alonso, plucked from Fiorentina in the summer of 2016, has been excellent since returning to the English game and forced Mat Ryan into fine blocks from a free‑kick and a header before flicking another Cesc Fàbregas corner into the far corner on the hour. That was his fifth goal this term and broke Brighton’s resistance for good on a day the hosts leant upon their Spanish contingent – Alonso, Fàbregas, Morata and Azpilicueta – to see them home. No club across Europe’s elite five leagues boasts more goals scored by Spanish players.

It was still Hazard who illuminated the occasion. His own standards rarely dip these days, even while team-mates labour in possession or in the pass. The 26-year-old has the speed of thought to unsettle even the most stubborn of rivals, with his scuttling presence alone enough to distract a resolute back line.

Chelsea’s problems tend to stem from opponents swarming around the playmaker’s every touch, which forces the collective ever deeper in their buildup play. At least they boasted an aerial threat here which eventually yielded a lead, Azpilicueta whipping in a centre beyond Lewis Dunk for Morata, in between centre-halves, to guide home via Ryan’s outstretched left hand.

Conte could bask in the onfield relationship which has been struck between ball-playing centre-half and No9. “Morata owes Azpi not one dinner, but many,” he joked. “And I want them to invite me, also.” He could afford to smile at the end, raising a glass of Champagne to wish the room a merry Christmas before departing with the gap to Manchester United in second place trimmed to a single point. One defeat in 11 league games would normally be cause for celebration, but Manchester City have warped accepted levels of excellence this term. The summit still feels distant.

Brighton had reason to curse their lapse of concentration and subsequent concession at a set play, and have their own problems in front of goal, having registered a solitary penalty in their meetings with the top six over the first half of the season. They had sacrificed some invention here, with Anthony Knockaert and Pascal Gross starting on the bench, but, for all their defensive discipline, were still rather too blunt for comfort and never came closer than Shane Duffy’s header which drifted wide of the far post.

Their more pivotal occasions will be against Newcastle and Bournemouth over the remainder of the festive period. January will see the pursuit renewed of a striker to supplement the ranks, though any move for Moussa Dembélé – Chris Hughton denied any contact with Celtic, rather than any interest – will surely be challenged by rivals. Chelsea, amongst others, have monitored the Frenchman’s progress since his switch north of the border from Fulham. If the Scottish champions will indeed listen favourably to offers in excess of £25m, plenty will consider the forward’s credentials.

“Particularly in January, what you’d like to do and what you can do can be different things,” said Hughton, whose moves for Vincent Janssen and Florin Andone had floundered on deadline day in August. “It’s a tough time to bring players in. Clubs don’t like losing players and their demands are high. But, if we can strengthen, we will.”

Brighton are 12th beyond the campaign’s halfway point and can be proud of their efforts so far, but their manager is well aware of the potential pitfalls ahead.