It took a goal six minutes from time by Nicky Barmby to finally break the hearts of brave Exeter.

They had defended magnificently and were given a standing ovation as they left the Goodison Park pitch by the home fans, reduced to just 16,000 on a bitterly cold night on Merseyside.

Everton were saved from humiliation by Barmby's late, late effort when he latched onto a deflected John Collins shot to drill the winner past Stuart Naylor.

The goal is priceless for Everton who are facing terrible financial problems. A Cup run is crucial to them, to boost their empty coffers.

Exeter fought for every inch, even if they produced a totally defensive display to thwart Everton's waves of attacks.

The Premiership side lacked pace and guile and were staring extra time in the face when Barmby struck.

It gives Walter Smith's boys a home fourth round tie with Birmingham next, but the feeling at the end was not of runs to Wembley but sheer relief that they had avoided a horror embarrassment on their own ground.

Exeter defended with nine across the pitch, and left only on loan West Ham kid Gary Alexander upfront, as the Devon side battled to keep Everton at bay.

Despite some tremendous defending from the Third Division side, 75 places below their Premiership rivals, Everton still contrived to create and waste 14 chances in the first period.

Francis Jeffers, back in the side after flu, could have had a hat-trick in that first period. Stuart Naylor rushed out to block a third minute chance for the teenager, who was later to nod agonisingly wide from a fine Mark Pembridge cross.

The teenager also drove an angled shot fractionally wide as Everton piled on the pressure.

Kevin Campbell stabbed one effort into the side netting and then saw a lob over Naylor drop wide of a post, as Everton fought with increasing desperation for the breakthrough.

Ironically, Exeter's only first half chance was by far the best of the opening period when Geoff Breslan charged down a Richard Dunne clearance and scampered away on his own to force a fine block from Paul Gerrard.

The story was the same after the break. Everton had all the possession, but could not create the big breakthrough.

Jeffers again, this time with a flicked header, forced Naylor into a plunging save to his right as the waves of attacks broke over Exeter's tireless defenders.

At times Exeter was unashamedly camped in their own area as Everton criss-crossed the face of the box with passes, probing for a gap to thread a telling pass through.

Jeffers spun on another Barmby pass, but his effort was blocked. Barmby, with an angled drive that flashed over and a Pembridge header, all failed to break Exeter's resistance.

Anxiety and frustration began to creep into Everton's play - along with mistakes and poor passing. All this gave Exeter increased heart, and Buckle, Chris Curran and Jason Rees fought for ever inch in front of their defence to halt Everton's progress.

The breakthrough, so cruel for Exeter, came in those last desperate minutes. Barmby was first to a loose ball as Collins' shot was deflected into the box. Barmby managed to drill an angled shot under Naylor's dive to see Everton home...red-faced and embarrassed.

Teams

Everton: Gerrard, Unsworth, Dunne, Weir, Cleland, Barmby, Hutchison, Collins, Pembridge, Campbell, Jeffers.

Subs Not Used: Ball, Watson, Moore, Simonsen, Cadamarteri.

Booked: Jeffers, Hutchison.

Goals: Barmby 85.

Exeter: Naylor, Power, Robinson (Flack 85), Gittens, Dewhurst, Richardson, Rees, Buckle, Curran, Breslan (McConnell 54), Alexander.

Subs Not Used: Smith, Boylan, Matthews.

Booked: Buckle, Robinson.

Att: 16,869

Ref: S Bennett (Orpington ).