Albion led twice at the London Stadium but had to settle for a point in a lively encounter against West Ham.
Neal Maupay put them ahead just before the break with his fifth goal of the season and after Ben Johnson equalised, Lewis Dunk scored for the first time since June with 20 minutes to go.
Tomas Soucek equalised for the second time from a corner and although they had to settle for a point, there were plenty of positives for Graham Potter ahead of two home games against Arsenal and Wolves, not least Maupay's return to the scoresheet and the fact that Albion profited from a set piece.
Potter made two changes with Dan Burn coming in for Joel Veltman and Danny Welbeck replacing Aaron Connolly, who felt his groin in training on Boxing Day.
It was Graham Potter's familiar 4-2-2-2 formation and Albion settled quickly into their stride with Danny Welbeck firing over from an angle and Maupay seeing a shot deflected for a corner during a bright start.
West Ham gradually worked their way into things and Jarrod Bowen had a decent chance in the 15th minute when Aaron Cresswell found him in space in the box but he volleyed well over.
That was the hosts' best moment of the first half as Albion bossed possession and won a lot of second balls, with Solly March at the heart of things. Welbeck was penalised for a foul as he attacked March's testing cross before March picked out Adam Webster with an out-swinging corner which the defender met with a firm header straight at Lukas Fabianski.
Burn then found March in lots of space down the left and he tried to beat Fabianski at his near post but found the side netting instead. Leandro Trossard then picked out Welbeck with a clever pass but Fabianski was out smartly to save at his feet as the striker stretched to make contact.
March threatened again, ghosting past Vladimir Coufal before forcing Fabianksi to save diving to his right and it was no surprise when he played a part in the opening goal on 44 minutes.
Found by Burn, he waited for the defender to overlap and Burn picked out Maupay on the edge of the six-yard box. His first shot was blocked but the Frenchman swooped on the loose ball when Declan Rice miscued his clearance and steered it inside the left-hand post.
Steven Alzate replaced Adam Lallana at the break and it was no surprise to see the hosts upping the tempo. Rice found Sebastien Haller with a decent cross and his header forced Rob Sanchez to make his first save of the contest.
But the keeper could do little to prevent Johnson from levelling on the hour. The visitors didn’t deal with substitute Andriy Yarmolenko's right-wing cross and when Manuel Lanzini laid it into his path, Johnson steered it expertly into the top right-hand corner, although Ben White very nearly managed to head it off the line as he flung himself in the path of the ball.
On the balance of play it was scarcely deserved and for the first time Albion were under pressure as West Ham began to get in crosses from both flanks, a familiar source of goals for them this season.
But with 20 minutes to go Albion went back in front thanks to Dunk. Trossard won a corner, found March and when Tomas Soucek tried to head clear it in the six-yard box he found Dunk who steered it home with his right foot.
Soucek made amend with eight minutes to go when West Ham levelled for the second time, powering home a close-range header from a right-wing corner by Cresswell.
It was a disappointing finale but a good point nonetheless for Albion.
Back on the goal trail
After four goals in his first five games Neal Maupay endured a nine-match barren run stretching 649 minutes in front of goal before his poacher's effort broke the deadlock at the London Stadium. Four of those five goals have been scored away from the Amex.
A sequence in the last nine matches between the teams of three West Ham wins, three Albion victories and three draws did not end as Albion would have hoped but in seven Premier League meetings West Ham have yet to beat Brighton.
Five of Lewis Dunk's seven goals in the Premier League have been scored from corners, while all seven have been netted from a set piece situation.
Sanchez, White, Webster, Dunk, Burn, March, Bissouma, Trossard, Lallana (Alzate 45), Maupay (Jahanbakhsh 90), Welbeck (Gross 84).
Subs not used: Steele, Mac Allister, Propper, Zeqiri, Bernardo, Veltman.
Referee: Simon Hooper.