Everton's James Beattie produced a rare magic moment in a dismal second hlf to dent West Ham's Champions League ambitions at Upton Park.
Looking for their sixth Premiership win in a row to lift them from eighth in the table, the Hammers were in front after just 10 minutes through Marlon Harewood's 13th goal of the campaign.
Leon Osman equalised but the Hammers went back in front with Dean Ashton's third goal in four appearances after 23 minutes.
But the home side lost their way in a dismal second half and could not muster a third goal after Beattie had cleverly lobbed a superb effort over goalkeeper Shaka Hislop with 20 minutes left.
Knowing they needed another victory to keep up the pressure on rivals Arsenal, who carved out a 4-0 win at Fulham, and Tottenham, who play Blackburn at White Hart Lane on Sunday, West Ham sent on Bobby Zamora and Teddy Sheringham.
They played for the closing 14 minutes but never looked like breaking down the Everton defence again.
Everton had lost only two of their previous 12 games in all competitions, and although rugged determination has been one of their key assets, David Moyes saw his side earn a point here with some ambitious counter-attacking.
Indeed they could have had a late winner but for Danny Gabbidon's heroic clearance over his own crossbar from a Mikel Arteta cross which was directed towards the attacking full-back Nuno Valente.
West Ham looked jittery at the back and were lucky not to be trailing in the opening minutes.
Hislop was relieved to see James McFadden's deflected shot go out for a corner from which Valente headed an inviting chance over the bar.
The home side shook off their nerves and with just 10 minutes on the clock Harewood struck emphatically, firing home from the edge of the penalty area from Yossi Benayoun's pass.
The lead was short-lived however, despite some slick attacking raids led by skipper Nigel Reo-Coker, winger Matthew Etherington and the industrious Hayden Mullins.
Full-back Lionel Scaloni was twice just too high with long-range drives before Arteta's pass perfectly set up Osman to blast a low drive beyond Hislop for an 18th-minute equaliser which Everton deserved.
But the visitors could not contain West Ham's attack for long. There was cultured football to enjoy in the game's third goal, which arrived in the 23rd minute.
Hislop's giant clearance was nodded on by Harewood and Ashton did the rest, bulldozing his way through in the inside left channel before lashing his shot past on-loan goalkeeper Sander Westerveld.
West Ham chased a third goal, putting the Merseysiders under heavy pressure for a spell.
Full-back Tony Hibbert was booked - on his return from suspension - for a bad foul on fleet-footed winger Etherington who was going clear down the left.
And if Harewood had made a return pass to Reo-Coker after his captain supported him with a run down the right it might well have been 3-1. Instead Harewood's shot from ambitious range was straight at Westerveld.
West Ham almost paid for that when Scaloni had to clear off the line after Hislop was beaten by Beattie's header five minutes before the break.
Then Beattie just cleared the bar with a rising shot before a header by Alan Stubbs from a far-post corner delivered by Arteta nestled safely in goalkeeper Hislop's arms.
There was a similar chance for Harewood soon after the interval, but he volleyed wide from Etherington's cross, and the opportunities dried up for West Ham after that.
Hibbert was lucky not to see red for Everton when he fouled Etherington again with a mistimed challenge, but referee Mike Riley gave him just a warning. Riley cautioned Arteta soon afterwards following a clash with Anton Ferdinand.
Everton stuck to their task and were rewarded when Beattie struck in the 71st minute after the ball fell kindly for him in the area.
He sized up the situation immediately and the quality of his finish left Hislop with no chance.
Frustrated West Ham fans began to get at their side after that but warmed to Gabbidon when the centre-back made his thrilling late intervention to prevent Everton sneaking all three points.
Teams:
West Ham Hislop, Scaloni, Ferdinand, Gabbidon, Konchesky,Benayoun (Zamora 76), Mullins, Reo-Coker,Etherington (Newton 87), Harewood, Ashton (Sheringham 84).
Subs Not Used: Bywater, Dailly.
Booked: Benayoun, Ferdinand, Scaloni.
Goals: Harewood 10, Ashton 23.
Everton Westerveld, Hibbert, Weir, Stubbs, Nuno Valente,Osman, Arteta (Kilbane 90), Neville, Cahill,McFadden (Davies 85), Beattie.
Subs Not Used: Turner, Naysmith, Carsley.
Booked: Neville, Hibbert, Arteta.
Goals: Osman 18, Beattie 71.
Att: 34,866
Ref: M Riley (W Yorkshire).