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:
5. Blades could hand Ndiaye new deal
Sheffield United could choose to reward youngster Iliman Ndiaye with a new contract following his recent progress, despite still being without a permanent manager following Chris Wilder’s departure last month. (The Star) (Photo by Laurence Griffiths/Getty Images) Photo: Laurence Griffiths
6. Brighton in for Styles
Brighton are readying a bid to bring Barnsley midfielder Callum Styles to the South Coast this summer, but will have to pay over £8million to make the move happen (The 72) (Photo by Clive Rose/Getty Images) Photo: Clive Rose
7. Jokanovic likely to move
Sheffield United target Slavisa Jokanovic is unlikely to stay at Al-Gharafa for another season, and wants to be reunited with his family in Europe. (The Star) (Photo by Alex Livesey/Getty Images) Photo: Alex Livesey
8. Leeds offered Moreno
Leeds United are in the hunt for 27-year-old left-back Alex Moreno. West Ham are also keen. (TeamTalk) (Photo by Fran Santiago/Getty Images) Photo: Fran Santiago