The Arne Slot roadshow keeps rolling on. Cody Gakpo’s double helped the Liverpool manager to make it seven wins from his first eight away matches in all competitions as the holders moved into the quarter‑finals despite making wholesale changes.

Slot could not have wished for a better start to life in English football and he rightly singled out the performance of the Czech goalkeeper Vitezslav Jaros, who made a spectacular save on his full debut when the game was finely poised at 1-0.

This was the first real setback for Slot’s opposite number Fabian Hürzeler since his arrival on these shores, with Brighton once again failing to get past this stage of the competition for the first time in approaching 50 years.

To their credit, they kept fighting and pulled one back through Simon Adingra and another through Tariq Lamptey after Luis Díaz seemed to have settled matters, but the hosts could not find a precious equaliser.

Slot expressed his concern this week about Liverpool’s lack of forward options after Diogo Jota was ruled out until after the next international break, with Federico Chiesa also sidelined. But with Gakpo in this kind of form, Slot may not need to worry as the Netherlands forward and several other fringe players made a strong case to be included from the start when Brighton are the visitors to Anfield on Saturday in the Premier League.

“I really liked what I saw for players who haven’t played much this season,” Slot said. “They were able to play a similar style and brought quality into the game. So that makes it even harder for me to select lineups for the upcoming weeks.”

Dominic Szoboszlai was tasked with leading the line here as Slot made eight changes from the team that drew with Arsenal on Sunday, with Mohamed Salah brought on as a late substitute when Brighton were threatening to find a way back into the game. The third-choice goalkeeper Jaros – wearing the No 56 shirt – rose to the occasion but it was a sign Liverpool were hanging on that Slot had to bring on Ibrahima Konaté to see out the last five minutes of injury time.

“We were not ruthless enough,” Hürzeler said. “Liverpool scored at the right moment – they had timing on their side and we were not able to reply.”

The Brighton manager said beforehand that there was no reason why his side should not target this competition given they have not got past this stage since 1979 when they lost against the eventual winners, Nottingham Forest, in the last eight. Yet having also made eight changes, the hosts seemed intent on giving their opponents a helping hand in the opening stages, with Szoboszlai nearly making Jason Steele pay for trying to play out from the back. Lamptey was denied early on by a good save from Jaros as Brighton’s second string looked keen to prove a point. Julio Enciso’s curler from 30 yards out had Jaros rooted to the spot as it dipped just over the crossbar.

Liverpool still looked dangerous on the break and Steele did well to save Szoboszlai’s shot with his legs after he had combined with Andy Robertson before Díaz headed the rebound wide. A slick move downfield ended with Robertson forcing Steele into another save at his near post. But given the number of changes on both sides, it was perhaps no surprise that they looked so disjointed.

Ferdi Kadioglu did not return for the second half because of a foot issue but it was down Brighton’s right flank that Liverpool found the breakthrough less than a minute after the restart. Tyler Morton latched on to a loose ball from a goal-kick and Gakpo did the rest, cutting in from the wing and unleashing an unstoppable shot into the top corner. Brighton would have been level immediately if it had not been for an outstanding reaction save from Jaros to somehow tip Adingra’s header from a Lamptey cross on to a post. Evan Ferguson then fired over from close range before Brajan Gruda was inches away with a curling effort from distance.

Liverpool were living on the edge but had a good chance to seal the win when Gakpo opted to set up Szoboszlai rather than shoot, which allowed Steele to make a save. There was no such unselfishness a minute later after the Dutchman beat the unfortunate Lamptey to the ball as he dispatched a low shot past the Brighton goalkeeper.

Brighton were handed a lifeline when Jarell Quansah misplaced a pass and Adingra bundled home from close range after Jaros had saved the initial shot. Díaz seemed to have ended any hopes of a comeback when he slammed home from Joël Veltman’s poor clearance but Lamptey’s deflected shot set up a nervy finale that Slot will be relieved to have come through.