Match ends, Everton 1, West Ham United 1.
- Everton relief as Lukaku nets 92nd-minute equaliser
- Hammers without a win in four matches
- Teams must replay at Upton Park next week
- Winners face Doncaster/Bristol City in round four
Romelu Lukaku fired in a late equaliser as Everton lifted the mood inside a gloomy Goodison Park with a dramatic FA Cup third-round draw against West Ham.
The Toffees were seconds away from their fifth successive defeat when the Belgium striker swivelled to volley in Bryan Oviedo's left-wing cross.
Defender James Collins put the Hammers ahead with a powerful near-post header from Morgan Amalfitano's corner.
Now the Premier League pair will meet in a replay at Upton Park next Tuesday.
The winners will travel to League One opposition in either Doncaster or Bristol City in the fourth round later this month.
Everton supporters greeted the final whistle with a relieved cheer as Lukaku kept the five-time winners in the competition with his first goal in seven matches.
But for long periods, it was another chastening experience for the exasperated home fans in a sparse 22,236 crowd.
The Toffees have lacked the energy and attacking spark that they showed in last season's promising debut campaign under Roberto Martinez, while being undermined by a frailty that sees them hold the second-worst defensive record in the Premier League.
And their dismal form looked set to continue when Collins was left unmarked, escaping Everton's zonal marking, to nod in his first goal of the season.
In contrast, the Hammers were moments away from reversing their fortunes after earning just one point from three top-flight matches over the festive period.
Sam Allardyce's men were comfortable for large periods with England international Stewart Downing instrumental from a central midfield role as the visitors looked to exploit any defensive uncertainty by Everton.
Downing's vicious 20-yard strike forced Everton keeper Joel Robles into a fingertip save, while both Matt Jarvis and Amalfitano almost turned in his teasing left-wing cross.
But, despite the Hammers edging possession and territorial advantage, the Toffees forged the clearest opportunities before half-time.
Lukaku had been almost anonymous for Everton in recent weeks, but he looked sharp and hungry as he twice threatened the Hammers goal with low shots.
The £28m summer signing looked likeliest to pose problems in an anxious second half for the home side, who also lost centre-back Sylvain Distin through injury.
Everton needed understudy keeper Robles to acrobatically stop Hammers striker Enner Valencia heading in a second - and that proved pivotal.
Lukaku finally broke through in the second minute of injury-time, netting for the fourth consecutive match against the Hammers, to leave Martinez jumping for joy on the Goodison touchline.
Everton manager Roberto Martinez:
"At the moment the cup is such an important competition for us it would have been a horrendous setback.
"It is very important we are still in the cup and now look forward to the next game in the league (at home to Manchester City) but still aware we are in a bad run.
"Romelu at his best will change games. We carry a different threat. I was really pleased with his attitude, showing real responsibility and maturity.
"In a period like ours you have two options, you can shy away and hide or you can take responsibility."
West Ham manager Sam Allardyce:
"That man (Lukaku) scores against us. Every time he plays against us he does. The disappointing thing was we didn't make it two when we had the chance.
"Enner Valencia's (header saved by Joel Robles), particularly, we should have scored.
"That would have made it 2-0 and it would have made it too much for Everton to come back."
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- 15DistinSubstituted forStonesat 71'minutes
- 17BesicSubstituted forMcGeadyat 85'minutes
- 11MirallasSubstituted forEto'oat 65'minutesBooked at 66mins
- 10LukakuBooked at 80mins
- 21AmalfitanoSubstituted forO'Brienat 78'minutes
- 7JarvisSubstituted forPoyetat 68'minutes
- 31E ValenciaSubstituted forColeat 60'minutesBooked at 88mins
- 12Vaz Te
- Anthony Taylor
- Shots on Target
Second Half ends, Everton 1, West Ham United 1.
Corner, Everton. Conceded by Diego Poyet.
Corner, West Ham United. Conceded by Bryan Oviedo.
Delay over. They are ready to continue.
Delay in match Winston Reid (West Ham United) because of an injury.
Goal! Everton 1, West Ham United 1. Romelu Lukaku (Everton) left footed shot from the centre of the box to the bottom right corner. Assisted by Bryan Oviedo.
Attempt missed. Seamus Coleman (Everton) header from the centre of the box misses to the right. Assisted by Bryan Oviedo with a cross.
Carlton Cole (West Ham United) is shown the yellow card for a bad foul.
Gareth Barry (Everton) wins a free kick in the defensive half.
Foul by Carlton Cole (West Ham United).
Attempt missed. Bryan Oviedo (Everton) left footed shot from the left side of the box misses to the left. Assisted by Aiden McGeady with a cross.
Attempt missed. Romelu Lukaku (Everton) left footed shot from outside the box is too high. Assisted by Steven Naismith.
Substitution, Everton. Aiden McGeady replaces Muhamed Besic.
Corner, Everton. Conceded by Adrián.
Attempt saved. Ross Barkley (Everton) left footed shot from the left side of the box is saved in the top centre of the goal.
Dangerous play by Carlton Cole (West Ham United).
Phil Jagielka (Everton) wins a free kick in the defensive half.
Romelu Lukaku (Everton) is shown the yellow card for a bad foul.
Winston Reid (West Ham United) wins a free kick in the defensive half.