When the final whistle blew under a wintry downpour at Stamford Bridge, players and coaching staff rushed onto the pitch as much in relief as celebration after the visitors pushed the Blues all the way in another roller-coaster game.
The 12 goals scored by Mauricio Pochettino's men in their last four games - against Tottenham Hotspur, Manchester City, Newcastle United and Brighton - have raised hopes among Blues fans that their long barren run in attack is behind them.
But the 11 they conceded show how far Chelsea still have to go to get themselves back among the Premier League's elite.
"Yes we have conceded but to win you need to score. That is entertainment, that is football. People love to see two offensive teams playing," Pochettino told reporters.
"Of course, I want to score 10 goals and to concede zero but if you want to be offensive, sometimes you take risks and concede chances. But it's about winning," he said.
Chelsea seemed set for a comfortable return to winning ways after last weekend's 4-1 hammering at Newcastle when Enzo Fernandez and Levi Colwill both scored their first league goals for the club in the 17th and 21st minutes.
Fernanadez's penalty strike in the 65th minute restored the two-goal cushion for the Blues, only for a late Joao Pedro header to set up the nervy finale which included a penalty for Brighton that was over-ruled after a VAR check.
Pochettino praised his young players for rising to the challenge of playing half the match with 10 men, even if he felt Gallagher did not deserve his second booking for a tackle from behind on former Chelsea colleague Billy Gilmour.
"I told them at halftime ... I am happy that that happened because it's a great opportunity for us," he said. "It's a massive challenge. Come on, now we need to show that we are a team. That is a thing that for sure will improve us."
Chelsea, who still sit 10 points off the top four in 10th spot, next face Manchester United away on Wednesday.
Brighton coach Roberto De Zerbi lamented the "three very stupid goals" his side conceded but refused to be drawn on the decision that James Milner fouled Mykhailo Mudryk which allowed Fernandez to score from the spot and make the score 3-1.
"About football, what you want, but about the referee (Craig Pawson) I didn't see nothing," said the Italian who has been given a touchline ban in the past for his conduct towards match officials. "We have to accept every decision."