Balogun scored the second quickest EPL goal by a substitute this season in the encounter when he came on for Pascal Gross in the 30th minute after Shane Duffy was sent off. The Ireland centre-back was sent-off for thrusting his head at Crystal Palace's Patrick van Aanholt directly in front of referee, Kevin Friend.
Murray had to be replaced by Andone and, after a brilliant goal-line clearance from Bernardo kept Milivojevic out, the Romanian punished Palace on the counter-attack in the fourth minute of stoppage time.
A Brighton fan has been arrested for throwing a pie at Wilfried Zaha during the Seagulls' victory over Crystal Palace.
West Ham also won 3-1 at home against Cardiff, while Bournemouth scored two goals in the first half to earn a 2-1 win over Huddersfield.
Murray returned to the starting line-up after being rested against Huddersfield and Andone's victor at the John Smith's Stadium may have made Hughton's decision tough to take. However, Roy Hodgson's side remain only three points above the bottom three.
Despite the loss of Duffy, Brighton still went on to win the game 3-1.
No one will know more than him that he can't get away with that.
- Brighton have lost just one of their last 10 Premier League games at the Amex Stadium (W5 D4), winning three of their last four (D1).
Balogun's goal is the second fastest goal by a substitute in Premier League history.
A Luka Milivojevic penalty just under 10 minutes from the end was Palace's consolation. They travel to Burnley for their next game on Saturday.