Marouane Fellaini struck the winner deep into extra-time as Everton finally saw off battling Stevenage in the Capital One Cup.
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The Belgian came off the bench to score in what could prove his final appearance for the Toffees at Goodison Park after 115 minutes of an absorbing second-round tie.
League One Stevenage had taken the lead against the run of play afer 36 minutes through Luke Freeman but debutant Gerard Deulofeu levelled just before the break.
Fellaini had received a good reception on his introduction despite continually being linked with a move to Manchester United before next week's transfer deadline.
Team-mate Leighton Baines, who is also interesting United, was an unused substitute but was also applauded as he warmed up.
With the transfer window due to close before Everton's next home game, it remains to be seen whether either play in blue at Goodison again.
Fellaini's close-range strike sent the Merseysiders through to a third-round clash with Fulham.
Yet Stevenage had proved tough opponents and almost snatched victory in the last minute of normal time through boyhood Everton Greg Tansey.
Everton made eight changes and handed out debuts to goalkeeper Joel Robles, defender John Stones and midfielder Deulofeu while Arouna Kone was given his first start.
They proved suprerior to Graham Westley's men in almost all departments - but their finishing let them down.
Ross Barkley was a brilliant driving force throughout for Everton and was always willing to shoot. He twice threatened in the opening minutes with one effort deflected and another flying over before David Gray somehow denied Kone from a yard out.
Stevenage gave warning when a swift break created a chance for James Dunne but Robles blocked and Jimmy Smith put the rebound over.
Normal service was soon resumed as Barkley charged forward and dragged a shot narrowly wide.
Stevenage suffered a blow when striker Darius Charles was forced off midway through the first half after a heavy challenge from Tony Hibbert.
Deulofeu, another constant menace to the Stevenage defence, went close when he shot across goal from a tight angle and the Spaniard then set up Leon Osman, only for the midfielder to miskick.
Everton were made to pay for their profligacy 10 minutes before the break when substitute Oumare Tounkara raced onto a long ball behind the home defence.
He pulled back for Smith, whose fluffed shot rolled perfectly for the inrushing Freeman to fire into the roof of the net.
Everton responded but Kone failed to win a penalty after claiming he had been tripped by Peter Hartley and then remarkably blasted over from 11 yards after linking with Steven Naismith.
The Toffees got the goal they deserved on the stroke of half-time as Deulofeu underlined his ability with a shimmy that took out two defenders and then passed the ball into the far corner.
Barkley continued his search for a goal after the break as he held off defenders on another storming run before exchanging passes with Bryan Oviedo and curling a shot at Chris Day. Day needed to be alert again to deny Kone from close range and Naismith was inches away from turning in a Deulofeu cross.
Barkley slumped to the turf in frustration after another fine effort rolled narrowly wide and Osman saw a chance deflected wide.
Deulofeu moved to the left and struck another goalbound shot from outside the area but Jon Ashton headed behind.
Everton fans showed frustration as Deulofeu shot straight at Day after another quick break six minutes from time. Barkley then shot over from the edge of the area and Gray's well-timed tackle denied Deulofeu another chance, although Everton appealed for a penalty.
Stevenage almost snatched victory in injury time as Tansey - grandson of former Toffees player Jimmy Tansey - forced Robles to tip over from 25 yards.
Fellaini entered the action to loud applause six minutes into injury time but the man he replaced, Barkley, deservedly received an equally good ovation.
Kone was agonisingly close to putting Everton ahead but Day brilliantly denied him twice from point-blank range in a goalmouth scramble.
It proved an uncomfortable moment for Gray, who slid legs apart into a goalpost attempting to dispossess Kone and required treatment.
Fellaini made his presence felt in the second period of extra-time but was brilliantly denied from 12 yards by a low Day save as Stevenage struggled to clear. The Belgian headed narrowly over from the resulting corner.
However, the Belgian settled the contest as the spectre of penalties loomed, pouncing after Roarie Deacon failed to clear a cross.