It is probably safe not to take Mauricio Pochettino’s description of himself as a university professor seriously. When this mess of a game was over Professor Poch was on the pitch, any illusion of thoughtfulness disappearing as he had a go at the officials, the elbow patches on his blazer well and truly off. Perhaps it is time for Todd Boehly to install a creche at Stamford Bridge. Pochettino was in charge of a class of unruly children during a performance that began with Chelsea in control and ended with Levi Colwill almost giving away a penalty in the 110th minute, tempers boiling over and Brighton almost snatching an unlikely point as chaos reigned.

Control? Composure? Forget about it. Chelsea have the worst disciplinary record in the top flight and were almost too intense in their pursuit of their fourth Premier League home win in 2023. They were up for a fight after their collapse against Newcastle but were down to 10 men when their captain, Conor Gallagher, got himself sent off just before half-time. Pochettino loved his young side’s spirit. He needs to fix the naivety, though.

Related: Chelsea 3-2 Brighton, Liverpool 4-3 Fulham: Premier League clockwatch – live reaction

“We have too many players who need to feel what it means to play in the Premier League,” Pochettino said, although he defended Gallagher and focused on the positives. “We needed to show our real face. We wanted to show we care.” The desire was captured by Thiago Silva making a crucial challenge as Brighton pushed for a late equaliser. Robert Sánchez made some important stops and the teams clashed after full time. “It is not just about your philosophy on the pitch,” Pochettino said. “You need to belong to the team. We needed this kind of game to challenge us.”

Chelsea also needed some good fortune. Brighton fumed at the VAR intervention that allowed Enzo Fernández to score the hosts decisive third goal from the spot. Later they would despair when Colwill was penalised for handball with Chelsea defending a 3-2 lead deep into added time, only for replays to show that the ball had struck the left-back in the face.

Jubilation turned to disappointment for Roberto De Zerbi, although Brighton’s manager chose not to complain about Chelsea winning a penalty for James Milner’s challenge on Mykhailo Mudryk. “I don’t want to speak about the referee,” the Italian said. “I didn’t see anything. I have to accept every decision.”

De Zerbi accepted that Brighton conceded silly goals. Chelsea responded to Pochettino’s anger after the 4-1 defeat by Newcastle. Pochettino made four changes, with Cole Palmer a notable omission, and reacted to a shortage of full-backs by naming Axel Disasi at right-back.

Chelsea were committed. Brighton, ravaged by injuries and weary after winning away at AEK Athens on Thursday, struggled to compete. It was too easy for Chelsea to play through midfield. Moisés Caicedo ignored the boos from the away end and offered control. Fernández was elusive. Raheem Sterling tested Brighton on the right.

The breakthrough arrived when Gallagher delivered a corner. Benoît Badiashile gathered possession and hooked the ball into the six-yard box. Brighton were vulnerable without Lewis Dunk at the back. Nobody tried to stop Fernández from heading in his first goal in the Premier League.

Soon it was 2-0. Nicolas Jackson headed Gallagher’s corner back into the middle and Colwill forced the ball over the line. It was the 20-year-old’s first goal for the club and it seemed that Chelsea were cruising, only for the mood to change when Adam Lallana found Facundo Buonanotte. One on one with Colwill, the winger cut inside and curled a beautiful shot past Sánchez.

Chelsea could have been clear – Mudryk had gone close – but now their inexperience took over. They were down to 10 men when Gallagher, who was fortunate only to receive a yellow for a foul on Buonanotte, lost Billy Gilmour and received his second booking for taking the former Chelsea midfielder down from behind.

It is worth remembering that Reece James, the club captain, was already unavailable after his dismissal against Newcastle. Pochettino has a problem. Silva took the armband but Caicedo was booked for kicking the ball away. Chelsea were edgy. Caicedo went close to being booked again and De Zerbi responded by introducing Kaoru Mitoma, João Pedro, Pascal Gross and Milner.

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Brighton were not stretching the 10 men. They lacked conviction and lost their shape after a corner. Jackson released Mudryk and Milner brought the winger down. Contact was slight, no more than a tangle of legs, but Craig Pawson gave a penalty after checking the pitchside monitor. Fernández extend Chelsea’s lead.

Chelsea fell back. Brighton still had time. Sánchez made a stunning stop from Gross and Brighton pulled a goal back when João Pedro headed in Milner’s corner. Now the nerves took over. Colwill had his escape and sheer desire got Chelsea over the line.