Brighton rued several missed opportunities and a disallowed goal by VAR as they were held to an entertaining 1-1 draw by West Ham.
The points were shared after two goals in four second-half minutes.
After Javier Hernandez broke away to give West Ham the lead with the visitors' first shot on goal, home debutant Leandro Trossard fired home a deserved equaliser.
Earlier, Trossard's fine volley past the excellent Lukasz Fabianski had been ruled out after a VAR check detected offside in the build-up.
Both sides had chances to claim victory during a breathless finale with substitute Michail Antonio nearly snatching a winner deep into injury time for the Hammers.
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Brighton made to pay for early profligacy - and by VAR
Trossard, along with everyone else in the Amex Stadium, thought he had marked his home debut with a goal after a splendid volley past Fabianski that would have given Brighton fair reward for a bright first half display.
But with the ball back on the halfway line, VAR detected that the right boot of Dan Burn had strayed into an offside position at the start of the attack and cut short Brighton's celebrations.
"Of course it's disappointing but if it is offside it is offside," reflected Brighton boss Graham Potter.
Despite five changes to the starting line-up thrashed by Manchester City on the opening weekend, West Ham lacked any sort of threat before the interval and Declan Rice produced the visitors' only shot of any description when he blazed over from the edge of the area.
At the other end, Fabianski was twice called upon to beat the ball away as Brighton offered a persistent threat.
The tone was set in the opening minutes when Burn headed over from close range and the defender turned provider for both Trossard's disallowed goal and another spurned opportunity which Glenn Murray put over the bar.
Jack Wilshere was replaced at half time by Antonio and the Hammers improved after the break, although Hernandez's goal still arrived very much against the run of play.
After Manuel Lanzini danced away from two challenges, Hernandez timed his run perfectly to latch on to Lanzini's through ball and calmly slot past Mathew Ryan.
But Brighton's response was almost immediate. After Glenn Murray prevented Issa Diop from clearing a long ball, the lively Trossard fired across Fabianski from the edge of the are and into the corner of the net.
As both sides went in search of a winner, Lanzini demanded a smart stop at his near post by Ryan and Antonio had a penalty appeal waved away by referee Anthony Taylor and by VAR.
But it was Brighton who squandered the clearest chance to claim victory when Davy Propper headed straight at Fabianski from close range.
Reaction from the managers
Brighton's Graham Potter: "I thought the performance was really, really good. The players kept going and I thought we played better than last week.
"We had a couple of chances and overall the performance level was really good. But we know we can improve.
"We went behind against the rule of play but we kept going. Disappointed with just one [point] but that's life. We still have a long way to go but the signs are good. Four points from two games is good but the performance is what we are focused on."
West Ham's Manuel Pellegrini: "We defended well but didn't create many chances. In the second half, our play improved.
"The first 45 minutes, Brighton created a couple of chances, but we needed to create better opportunities.
"We have a lot of different options now. It was important not to lose today. It was important because we were playing away and we were coming off the back of a defeat. Two defeats in a row would have been very similar to last season and a difficult start.
"I thought a draw was the right result and deserved by both teams.
"We must continue to try to improve our offensive play."
Man of the match - Dan Burn
Could have opened the scoring in the opening minutes and his stray foot was the reason why Brighton's first-half 'goal' was ruled out, but Burn was a powerful presence throughout and produced several searching crosses that, on another day, could have assisted the hosts to three precious points.
Brighton host Southampton next Saturday, kick off at 3pm, while West Ham travel to Watford.