After Jérémy Doku's second-half substitute appearance transformed Manchester City into a high-octane proposition, the smart money was on the momentum continuing into a victorious penalty shootout.

So it proved as Enzo Maresca's men triumphed 4-3, Gerónimo Rulli the hero: his save from Lewis Dunk's fifth spot-kick was decisive, the Argentinean also having repelled Yasin Ayari's fourth effort.

While Jason Steele kept out Mateo Kovacic's attempt, City progressed after Brighton twice took the lead – via Malick Yalcouyé and Georginio Rutter – before being pegged back by Kovacic and Vitor Reis.

Maresca was left beaming: "Since I'm here we never practised penalties," said the City manager. "It always happens that the one that scored in the 90 minutes [Kovacic] misses the penalty. I am very happy."

Of Doku, he said: "He made an impact. This is the reason they are there. Jérémy and the rest – to try to do their best, if they start from the beginning or if they come in from the bench try to make an impact."

The tie might have gone either way, so the lottery of penalties felt apt to decide who went through before Saturday's rematch back here in the league. City will now play League One Bradford in the quarter-finals.

"I watched all [Brighton's] Premier League games and since the first day they always go front foot, man to man, so they're going to be exactly the same on Saturday," Maresca said.

His opposite number spoke of vengeance. "We lost in a shootout. We had enough chances to win the game – they had the luck today. We have to reset. We have a great chance on Saturday to take revenge," said Fabian Hürzeler.

Brighton will stay up in the area. "Not sleeping in your own bed is not an advantage," said the manager. "But we'll go there with full energy and ready to go on Saturday."

When Yalcouyé opened the scoring there was the proverbial hint of offside about the forward as his shot pinged off Rulli and in.

With no video assistant referee in the Carabao Cup the goal stood, though it was soon cancelled out by Kovacic: Phil Foden fed him and, from the edge of the penalty area, he threaded the ball beyond Steele low into the left corner.

For the second half Maresca introduced Rayan Aït-Nouri and Ryan McAidoo for Ayyoub Bouaddi and Floyd Samba. Instantly, though, City conceded: Brighton slipped through the lines with ease, and Jaouen Hadjam's cross was slid in by Rutter.

The forward's grin went wide in celebration and the Seagulls were heading through, while City were going out. Aït-Nouri, skipping down the left, tried to do something about this, but his ball over was aimless.

At least there was pace in this foray, which those in blue sometimes lacked. But, also, Maresca's team had become sloppy – a long-range Rayan Cherki pass that ended in Steele's gloves was emblematic.

Olivier Boscagli's corner that dipped viciously close to Rulli's goalline was far more dangerous, so just after the hour Maresca introduced a first big gun – Doku, for Allan – this coming after Rutter ran in and went close to a second, underlining Brighton's ascendancy.

When Doku played Aït-Nouri in through the left, it was a rare City attack and showed the value of having the Belgian now able to affect the game.

At this point, though, the decision to allow his star quintet the night off was backfiring for Maresca. City lacked control and were toothless. Doku, again, cut through Brighton but there were no runners to prosper from his delivery infield.

Hürzeler's men tried to squeeze time and snaffle the ball whenever City attempted to move them about, but then came a first passage in which City camped in Brighton territory. Suddenly, those in green were having to answer questions. Foden's burst that drew a free-kick from Rutter near the 18-yard line presaged one they could not answer. Cherki blasted at goal, Reis stuck out a boot, Steele was wrongfooted, and it was 2-2. Doku had lit up City, his presence terrorising Brighton's defence and turning the tie.

"They are in a brilliant moment, scoring goals, many goals every game and winning, so we knew it was a tough game in terms of defending in the right way," Maresca said. "We could have probably done something better defensively, but we started just three months ago [together]. The game was chaotic but we controlled it quite good."