After weathering an early storm and losing a lead they scarcely deserved, Walter Smith's team took control in the second half and should have put the tie beyond Huddersfield's reach.
The Yorkshiremen came into the match on the back of four straight wins which had taken them to the top of the First Division, and they had clearly decided their best hope was to keep their foot hard down on the throttle.
The Terriers laid siege to Thomas Myhre's goal for the first half hour, pinning Everton back with a mixture of one-touch football and long balls aimed at their in-form strike partnership of Marcus Stewart and Wayne Allison, who had already chalked up half-a-dozen goals apiece.
Stewart almost stole his seventh when he beat the offside trap only to be denied by Myhre racing off his line, and he sent a header and a 30- yard snap shot past the woodwork before Everton threatened on the break.
Everton stole the lead after 36 minutes when Dave Watson went forward for a corner and met Duncan Ferguson's flick with a powerful header beyond Nico Vaesen.
That goal against the run of play briefly unsettled the home defence and Vaesen had to make a one-handed save from Nick Barmby, but it was a defensive blunder at the other end that brought Huddersfield the goal they deserved.
Myhre failed to cling on to Steve Jenkins' deep cross and Allison stabbed home the loose ball on the stroke of half-time.
Walter Smith, the Everton manager, administered a much-needed lecture and the transformation was remarkable. Suddenly the Terriers were at bay and only a combination of desperate defending and deplorable finishing kept them in the tie.
Marco Materazzi contrived to stab Oliver Dacourt's cross wide of the far post from just inches out, Vaesen dived to his left to claw down a Don Hutchison header and defender Kevin Gray blocked Ferguson's 20-yard drive on the line.
"Our first-half performance wasn't good, but we turned it round in the second," said Smith.
Peter Jackson, the Huddersfield manager, said: "If we give the ball away like we did in the second half at Goodison, we will get hammered."
Huddersfield Town (4-4-2): Vaesen; Jenkins, S Collins, Gray, Edwards; Dalton, Johnson (Browning, 82), Horne, Thornley (Beresford, 71); Stewart, Allison. Substitutes not used: Barnes, Francis (gk), Dyson.
Everton (4-4-2) : Myhre; Cleland, Watson, Materazzi, Unsworth; Hutchison, Dacourt (Madar, 82), J Collins, Ball; Barmby (Cadamarteri, 74), Ferguson. Substitutes not used: Farrelly, Gerrard (gk), Tiler.
Referee: U Rennie (Sheffield).Reuse content