And that could be enough for Europe next season.
Four points from their last two games will secure at least seventh place.
They could even target fifth after Aston Villa only drew 2-2 at Burnley.
Everton are now four points behind the seventh-placed Seagulls after drawing 2-2 at Selhurst Park and their boss David Moyes said Europe is drifting away.
His side twice lost the lead to follow their last-gasp loss of two potential points in the 3-3 draw with Manchester City on Monday.
“I’ve enjoyed talking about Europe,” said Moyes. “It’s making Everton supporters dream again, and me, hopefully that it could happen again.
“I’d hoped we can get us to a level where we can be competitive again at European level. It’s not gone yet but it’s drifting away from us at the moment.”
By the time Albion play next, the European race will be a little clearer because we will know which team have won the FA Cup.
Their next opponents Leeds are safe after West Ham lost 1-0 at home to Arsenal.
Newcastle can no longer catch Albion after their 1-1 draw at Nottingham Forest and it is highly unlikely Crystal Palace will either.
Everton, Sunderland, Fulham, Chelsea and Brentford all lost ground on the Seagulls over the weekend but the latter are only two points adrift.
Albion, in turn, trail sixth-placed Bournemouth by two points.
Fabian Hurzeler’s men have an advantage over all their closest rivals in the goal difference column.
Brentford host Palace on Sunday while Albion are taking on Leeds at Elland Road.
Bournemouth do not play until a week on Tuesday, when Manchester City head south.
Villa and Liverpool are both five points above Albion and play each other on Friday.
The Seagulls will hope that game does not end in a draw and would need to beat both Leeds and Manchester United to climb above the losers.