That result meant that the Seagulls have now lost just one of their last four Premier League outings, with West Brom the only other side in the bottom half of the table who can match their points haul over the course of that spell. This weekend – or next Tuesday evening, to be exact – Albion come up against Chelsea at Stamford Bridge.
Brighton haven’t beaten the Blues since 1933 – a victory that remains their sole triumph over the west Londoners.
If the Seagulls are to get anything in the capital, however, midfielder Yves Bissouma is likely going to have to be on top of his game.
Speaking about the Malian after his side’s stalemate against the Toffees, Albion boss Graham Potter said: "He's tried very hard to understand what we are trying to do as a team.
"He's been playing in the role often so he understands what he has to do.
"Adam (Lallana) plays an important role alongside him as well as Pascal [Gross] and Lewis Dunk behind him.
"They help him. He's taken his game forward. We knew the quality he had. It's about getting that consistency."
Bissouma is expected to be in demand this summer.
Sky Sports pundit Jamie Carragher recently said: "I think teams will be looking at him.
"I think they will be bidding for him at the end of the season."
Here are today's biggest transfer stories and the latest team news involving Brighton and the rest of the Premier League, as the reaction to last weekend's action continues:
1. Dragusin rejects Toon
Juventus defender Radu Dragusin has rejected offers from Newcastle United and Tottenham, according to his agent. (TuttoJuve) (Photo by Chris Ricco/Getty Images) Photo: Chris Ricco
2. Liverpool favourites for Bissouma
Liverpool have emerged as favourites to sign Brighton midfielder Yves Bissouma this summer, according to bookies. (Sky Bet) (Photo by Mike Hewitt/Getty Images) Photo: Mike Hewitt
3. Palmer rules out Wilson exit
Former Premier League midfielder Carlton Palmer has claimed that he cannot see Newcastle United striker Callum Wilson moving to a club like West Ham in the summer. (Football FanCast) (Photo by Stu Forster/Getty Images) Photo: Stu Forster
4. Whites want Gutierrez
Leeds United are also keeping tabs on Real Madrid’s Miguel Gutierrez as they look to add quality cover and competition at left-back. (TeamTalk) (Photo by Quality Sport Images/Getty Images) Photo: Quality Sport Images