An incredibly uneventful first period in the English capital only produced two shots on target - one from each side - and it was certainly not a half that will live long in the memory.
The breakthrough finally arrived early in the second period, with Wieffer converting from close range after Lewis Dunk's challenge had forced West Ham goalkeeper Lukasz Fabianski into a weak punch.
West Ham were only behind for six minutes, though, with the leveller arriving in the 57th minute through Kudus, who headed into the back of the net from close range after Brighton goalkeeper Bart Verbruggen found Jarrod Bowen's strike to be too hot to handle.
That was to be the end of the scoring at the London Stadium, as the two teams shared the points, with West Ham remaining in 14th spot in the Premier League table, while Brighton stay ninth, now five points off the top four.
SPORTS MOLE'S VERDICT
The opening 45 minutes of football produced little of note, and at that stage, it did appear that a goalless draw was on the cards.
Brighton struck first, with Wieffer converting from inside the box, and that opener raised the tempo, with West Ham starting to look a threat going forward, and they managed to level courtesy of a header from Kudus.
It was clear that neither wanted to take many risks from that point forward in fear of suffering a defeat, though, and neither did enough to deserve all three points at the conclusion of the contest.
In the end, a point each was about right, and both managers can be content with the draw, but West Ham's position of 14th is hardly attractive, while just five wins from 17 Premier League matches this season is disappointing.
Brighton, though, are up in the top half and within touching distance of the top four, so it has been a successful campaign to date for the Seagulls, who have only been beaten on four occasions in England's top flight this term.
WEST HAM VS. BRIGHTON HIGHLIGHTS
51st min: West Ham 0-1 Brighton (Mats Wieffer)
Brighton take the lead in the 51st minute of the contest, as Wieffer taps into the back of the net from inside the box after West Ham goalkeeper Fabianski lost out in a battle with Brighton captain Dunk.
57th min: West Ham 1-1 Brighton (Jarrod Bowen)
West Ham level the scores in the 57th minute of the contest, as Kudus heads into the back of the net from close range after Brighton goalkeeper Verbruggen kept out a powerful drive from Bowen.
All square in the English capital with more than 30 minutes left to play.
MAN OF THE MATCH - MOHAMMED KUDUS
Kudus scored the leveller for West Ham, and he was the most threatening player on the field, with almost all of the home side's strong work on Saturday afternoon coming from the 24-year-old.
The forward was such a big threat in the final third, but he also helped his side out defensively, making four tackles, and it is not difficult to understand why a number of major clubs are said to be tracking him.
WEST HAM VS. BRIGHTON MATCH STATS
Possession: West Ham 46%-54% Brighton
Shots: West Ham 11-12 Brighton
Shots on target: West Ham 4-6 Brighton
Corners: West Ham 8-4 Brighton
Fouls: West Ham 14-20 Brighton
WHAT NEXT?
West Ham will be bidding to stretch their unbeaten run in the Premier League to four matches when they head to struggling Southampton on Boxing Day.
Brighton, meanwhile, will aim to end a five-game winless run in England's top flight when they host Brentford on December 27.
Written by
Matt Law