The Arne Slot Roadshow continues to impress. Cody Gakpo's quick brace helped the Liverpool manager to seven wins from his first eight away games in all competitions, helping the defending champions reach the quarter-finals despite major changes on the south coast.

Slot couldn't have asked for a better start to life in English football and he will have been mightily impressed by the performance of Czech goalkeeper Vitezslav Jaros, who made a spectacular save on his debut when the game was finely balanced at 1-0. This was the first real setback for his counterpart Fabian Hürzeler since his arrival on these shores, as Brighton failed to progress past this stage of the competition for the first time in almost 50 years.

To their credit, they continued to fight, scoring a goal from Simon Adingra and another from Tariq Lamptey after Luis Díaz appeared to have sorted things out, but the hosts were unable to find a valuable equalizer ahead of their trip to Anfield at the weekend.

Slot expressed concern this week about Liverpool's lack of striker options after Diogo Jota was ruled out until after the next international break and Federico Chiesa was also sidelined. That meant Dominik Szoboszlai was tasked with taking charge, while Mohamed Salah was one of eight changes from the side that drew with Arsenal on Sunday. Third-choice goalkeeper Jaros – who wore the number 57 shirt – made his full debut, while Tyler Morton started alongside Wataru Endo and Curtis Jones in central midfield.

Any Brighton fans still reeling from the late goals conceded against Wolves on Saturday would have been happy if Evan Ferguson had been given another chance after an 11-month goal drought. Hürzeler – who also made eight changes, including a first start for the lively Brajan Gruda, a £25million summer signing from Mainz – said there was no reason why his side shouldn't target this competition since They have not survived this phase since 1979, when they lost in the quarter-finals to eventual winners Nottingham Forest.

However, Brighton appeared keen to give their opponents a leg up in the early stages, with Szoboszlai almost making Jason Steele pay for trying to play out from the back. It was Joe Gomez who was caught napping as Jan Paul van Hecke's goal-line ball hit Adingra and Lamptey raced towards his pass. But to the relief of a crowded away team behind his goal, Jaros had his shot saved.

Brighton's second team appeared eager to prove a point as they battled for starting places under their young manager and enjoyed more possession as the first half progressed. Julio Enciso's curler from 30 yards out left Jaros standing in his tracks as it bounced just over the crossbar. Liverpool still looked dangerous on the counter-attack and Steele parried Szoboszlai's shot with his legs after combining with Andy Robertson before Luis Díaz headed the rebound wide. In another rare moment of quality that brought Slot to his feet in the technical area, a clever break downfield ended with Robertson forcing Steele into another save at his near post. Given the number of changes on both sides, it was perhaps no surprise that they seemed so disjointed.

Ferdi Kadioglu did not return in the second half, but Liverpool made a breakthrough down Brighton's right flank less than a minute after the restart. Morton grabbed a loose ball from a goal kick and Gakpo did the rest, cutting inside from the wing and firing an unstoppable shot into the top corner. Brighton would have equalized straight away had Jaros not made an excellent reaction to somehow direct Adingra's header onto the post from Lamptey's cross. Ferguson then fired over from close range before Gruda shot just inches away from distance.

Liverpool were on the verge of danger, but when Lamptey lost the ball they were presented with the perfect opportunity to calm their nerves. Suddenly Gakpo was pushing for the goal, but he decided to pass on Szoboszlai instead, allowing Steele to save. There was no such selflessness a minute later after the Dutchman beat the unfortunate Lamptey to the ball: the ball flew into the net after Gakpo hammered it low past the Brighton goalkeeper.

Brighton were given a lifeline when Jarell Quansah misplaced a pass and Adingra fired home from close range after Jaros had parried the initial shot. Díaz appeared to have dashed any hopes of a comeback when he fired home after a poor free throw from Joël Veltman, but Lamptey's deflected shot made for a nervy finale that Slot will be relieved to have survived.