Match ends, Stevenage 0, Everton 4.
Everton eased into the fifth round of the FA Cup as League One strugglers Stevenage were comfortably beaten at Broadhall Way.
Steven Naismith scored twice in the first half to put the Toffees in full control before substitutes Johnny Heitinga and Magaye Gueye added gloss to the scoreline for Roberto Martinez's side after the break.
But Everton's satisfaction will be tempered by a serious injury to Bryan Oviedo.
The 23-year-old Costa Rican was stretchered off in the first half after suffering a double leg break while trying to block Simon Heslop's shot.
Players from both sides immediately indicated the severity of the versatile player's injury.
That setback apart, Everton coped well with a playing surface that was far from perfect to complete the job in a highly-professional manner and maintain Martinez's hopes of retaining the trophy he won with Wigan Athletic at Wembley last season.
Stevenage's best chance came in the opening moments when Everton keeper Joel Robles could not collect a long ball but Lucas Akins saw his goalbound shot blocked by retreating defender John Stones.
Everton punished Graham Westley's side almost immediately when Kevin Mirallas's shot was turned away but Aiden McGeady recovered the ball to set up Scotland international Naismith for a simple finish.
Oviedo's injury forced a six-minute delay and there was sympathy all around the stadium as he was carried off.
Stevenage's early momentum had disappeared and Everton effectively wrapped the game up in the 32nd minute when Naismith pounced on a mistake by Jon Ashton to beat keeper Chris Day in composed fashion.
While Johnny Heitinga may yet leave Goodison Park before the transfer window closes on 31 January, the Dutchman was on target within 10 minutes of coming on as a half-time replacement for skipper Phil Jagielka
The Netherlands defender headed home an acrobatic overhead cross from the left by Mirallas, who had posed problems for the Stevenage defence throughout.
And as Everton closed out the formalities, Gueye gave the scoreline an even more emphatic appearance with six minutes left, riding challenges from Leon Osman's pass to roll in his finish.
Stevenage had occasionally troubled Robles and it took Heitinga to rescue Everton in a scramble at the death as both Roarie Deacon and Dean Parrett failed to turn in the loose ball.
Everton manager Roberto Martinez:
"We wanted as professional a performance as we could and that's as professional as it gets.
"It was a real test and we always looked a threat on the counter. It was a performance that was as good as it gets when you take it all into consideration.
"We were brave, really attacking but the incident with Bryan affected everyone. Those injuries give you a bad taste.
"Steven Naismith is someone who has played that position with Scotland and he has very good movement. He showed what he can do."
- 6JonesSubstituted forParrettat 72'minutes
- 29HartleyBooked at 38mins
- 7MoraisSubstituted forAndradeat 81'minutes
- 20SmithBooked at 60mins
- 12ZokoSubstituted forDeaconat 85'minutes
- 6JagielkaSubstituted forHeitingaat 45'minutes
- 14NaismithBooked at 63mins
- 11MirallasSubstituted forGueyeat 81'minutes
- 8OviedoSubstituted forOsmanat 22'minutes
- Anthony Taylor
- Shots on Target
Second Half ends, Stevenage 0, Everton 4.
Attempt missed. Lucas Akins (Stevenage) left footed shot from outside the box is too high.
Attempt saved. Dean Parrett (Stevenage) right footed shot from the centre of the box is saved in the centre of the goal.
Attempt saved. Darius Charles (Stevenage) right footed shot from the right side of the box is saved in the centre of the goal. Assisted by Peter Hartley.
Leighton Baines (Everton) wins a free kick in the defensive half.
Foul by Darius Charles (Stevenage).
Substitution, Stevenage. Roarie Deacon replaces Francois Zoko.
Goal! Stevenage 0, Everton 4. Magaye Gueye (Everton) left footed shot from the centre of the box to the bottom right corner. Assisted by Leon Osman with a through ball.
Substitution, Stevenage. Bruno Andrade replaces Filipe Morais.
Substitution, Everton. Magaye Gueye replaces Kevin Mirallas.
Offside, Everton. Gareth Barry tries a through ball, but Kevin Mirallas is caught offside.
Corner, Stevenage. Conceded by Joel Robles.
Corner, Stevenage. Conceded by Tony Hibbert.
Offside, Stevenage. Darius Charles tries a through ball, but Francois Zoko is caught offside.
Substitution, Stevenage. Dean Parrett replaces Luke Jones.
Attempt missed. Francois Zoko (Stevenage) right footed shot from the centre of the box is close, but misses to the right. Assisted by Luke Freeman with a cross.
Attempt blocked. Aiden McGeady (Everton) left footed shot from the centre of the box is blocked. Assisted by Kevin Mirallas.
Attempt missed. Leighton Baines (Everton) left footed shot from outside the box is too high from a direct free kick.
Kevin Mirallas (Everton) wins a free kick on the left wing.