When it finally arrived the goal could not have been more out of keeping with Chelsea’s recent attacking efforts. There was a deft assist from Cole Palmer, who impressed on his first start since joining from Manchester City, but what stood out even more was Nicolas Jackson casting the doubts aside, taking the ball on the run and finding the ruthlessness to send Brighton out of the third round of the Carabao Cup.

Was this really Chelsea? It has not been easy to keep the faith with Mauricio Pochettino’s blunt side. Chelsea, who had gone three games without finding the back of the net, had felt the gloom deepening after losing to Aston Villa. There were even concerns that the men’s team would not be contributing any entries to the club’s goal of the month competition for September.

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Yet Pochettino has kept talking up the positives. He has leaned on the data, using it as proof that performances have been better than results suggest, although it is easier to feel optimistic when the flashes of youthful promise are accompanied by substance in both boxes. Jackson, in particular, had a point to prove after infuriating Pochettino with his foolish booking against Villa. The hope will be that the striker benefits from making Brighton regret their early profligacy.

“A good response from the team,” Pochettino said. “I am happy for the victory and it is important to go through to build our momentum. I am very pleased for Jackson. For a striker to score is very important. He needed to feel the net.”

• Mansfield v Port Vale

• Ipswich Tv Fulham

• Manchester United v Newcastle

• Bournemouth v Liverpool

• Chelsea v Blackburn

• West Ham v Arsenal

• Everton v Burnley

• Exeter v Middlesbrough

Ties will be played on 31 October and 1 November

Pochettino could also take heart from how Chelsea recovered from a shaky start, particularly with Marc Cucurella excelling as a stand-in right-back and Palmer’s creativity catching the eye. A clean sheet was a boost, Robert Sánchez’s saves frustrating his former side, and the only negative was Ben Chilwell limping off with a hamstring injury in added time.

Chilwell’s exit left Chelsea with 10 men and was followed by João Pedro volleying narrowly over. An equaliser would not have flattered Brighton, even if they were fortunate not to go 2-0 down when Jackson had a second goal wrongly disallowed for offside. “We played a good game,” Roberto De Zerbi said. “We have to score and kill the game.”

If news of the injured Reece James being charged by the Football Association for allegedly abusing a match official after the Villa game was not enough to hammer home the sense of uncertainty at Chelsea, then perhaps it was in how uncoordinated they looked compared with Brighton for much of the first half.

The biggest problem came when the ball was with Sánchez – a weakness that came as little surprise to Brighton. There was a reason why De Zerbi cast the goalkeeper aside last season. Brighton targeted their former keeper and only shoddy finishing spared Chelsea, who host Blackburn in the next round. João Pedro chipped over after intercepting a pass from Sánchez, who would later save well from Ansu Fati after playing Moisés Caicedo into trouble.

De Zerbi was not entirely pleased with Brighton’s display, though. Kaoru Mitoma was quiet against Cucurella and there were openings for Chelsea. Palmer went close and Mykhailo Mudryk, lively but inconsistent on the left, could have had a penalty.

Chelsea were on top as half-time approached. While Lesley Ugochukwu was fortunate not to be sent off after a risky foul, Caicedo was having a strong game against his old side. The £115m midfielder had an engaging battle with Carlos Baleba, the youngster Brighton signed as his replacement.

The visitors had lost their way and replaced Fati with Solly March. Yet the loose balls were going Chelsea’s way. Ugochukwu became increasingly authoritative in defensive midfield, pushing Brighton back.

Chelsea earned their reward after 50 minutes. Jan Paul van Hecke and March lost possession and the ball reached Ian Maatsen on the right. An overload developed and Palmer took over. He took his time, rolling a foot over the ball before slipping it through for Jackson to sweep a low finish beyond Bart Verbruggen.

The flag stayed down and Jackson, who is banned for Monday’s trip to Fulham, could celebrate. Chelsea dug deep. Brighton pushed for an equaliser, Sánchez repelling March’s header, but Chelsea had too much conviction.