Mark Noble got his first senior West Ham goal as last year's FA Cup finalists edged into round four at the expense of League One outfit Brighton.
Noble celebrates his first senior goal for West Ham
Despite being separated by 41 league places, there was little to choose between the sides in the first half.
However, the Hammers took control after Noble latched on to Carlos Tevez's knockdown to fire home from 18 yards.
Carlton Cole then made it two from debutant Luis Boa Morte's cross, before Hayden Mullins' late header sealed it.
It was a welcome victory after three straight defeats for West Ham, even if it took until the second half for them to stamp their authority on the contest.
With Nigel Reo-Coker, linked with a move to Tottenham, conspicuous by his absence, the hosts struggled to hit their straps in a first half notable mainly for referee Mark Halsey's refusal to give a penalty for Joe O'Cearuill's clumsy challenge on Boa Morte.
However, Tevez, who increasingly looks to be finding his feet in England, was lively throughout and was denied only by Dean Hammond's brave block in the early stages, while Alexandre Frutos looped Brighton's best effort onto the roof of the net.
With both sides clearly bereft of confidence - Brighton themselves had suffered four straight defeats before the game - the first goal was always going to be crucial and so it proved when Noble drilled in after Tevez had cleverly knocked down George McCartney's cross.
Thereafter, the Hammers took control and it was little surprise when Cole doubled the lead on the volley from Boa Morte's whipped cross, although Brighton were aggrieved that an offside flag was not shown against the striker.
Brighton struggled to rouse a late rally and, with virtually the last touch of the game, Mullins rose unmarked in injury time to head home Shaun Newton's cross to seal the hosts' victory and leave the visitors still searching for a first third-round win in 14 years.
West Ham manager Alan Curbishely:
"We needed a result for sure. From the outside this probably looked like a potential upset and it was a difficult game, but the first goal settled us and we were comfortable in the end.
"There's nothing to read into my team selection, other than I wanted to look at some players I haven't seen yet. I need to evaluate my squad as soon as possible.
"I am certainly disappointed with the way some of my recent comments have been reported, and I'm upset at the treatment of Nigel Reo-Coker as well. I want club and fans to pull together as one to help get us out of our situation."
Brighton boss Dean Wilkins:
"We felt the longer the game went on the quieter the crowd would be and then if we did score they would get on West Ham's backs.
"If we'd been a little bit calmer then we could have scored first. Was it naivety, the occasion? I do not know.
"That was slightly disappointing, but as long as they learn from their mistakes there's no problem at all."
West Ham: Carroll, Dailly, Ferdinand (Spector 45), Gabbidon, McCartney, Benayoun, Mullins, Noble, Boa Morte (Newton 73), Cole (Zamora 68), Tevez.
Subs Not Used: Green, Sheringham.
Goals: Noble 49, Cole 58, Mullins 90.
Brighton: Henderson, O'Cearuill, Lynch, Butters, Mayo, Fraser (Hart 51), El-Abd, Hammond, Frutos (Rents 67), Revell (Gatting 84), Robinson.
Subs Not Used: Kuipers, Carpenter.
Booked: Mayo, El-Abd.
Ref: M Halsey (Lancashire).