Marouane Fellaini came off the bench to fire Everton into third round of the Capital One Cup with an extra-time winner against League One Stevenage at Goodison Park.
The Belgian's 115th-minute strike came against the backdrop of yet more speculation linking both him and team-mate Leighton Baines with moves to Manchester United.
It secured a 2-1 win after Everton debutant Gerard Deulofeu had scored a superb equaliser to cancel out Luke Freeman's shock 36th-minute opener for Stevenage.
With next week's transfer deadline coming before Everton's next home game, Fellaini's dramatic late effort could prove his final act in a blue shirt at Goodison.
Everton last week rejected a £28million joint bid for Fellaini and Baines from Old Trafford and are now bracing themselves for an improved offer.
The Belgian's value to the Toffees was evident as he picked up a tiring side that had squandered a host of chances to kill off Stevenage.
He had already forced one good save from Chris Day and headed narrowly over when he struck after Roarie Deacon failed to clear a cross.
Manager Roberto Martinez, for whom the win was his first since taking charge, said: "When Marouane Fellaini went on to the pitch he really gave us the push we needed.
"I felt we deserved to go through, which is what matters, but I feel the headlines should go about how well Stevenage played and how well they pushed us right to the end."
Such headlines might be unlikely following a report claiming that Baines has asked if he can leave the club and another suggesting United are now preparing a £38million joint bid.
Despite that Fellaini and Baines, who was an unused substitute, both acknowledged good applause from the crowd and Martinez was dismissive of the latest stories.
He said: "I am not going to entertain any rumours or speculation.
"When there is anything to tell our fans, we will tell them.
"At the moment we are still looking from a different perspective, we are trying to get one or two bodies in and we focus on the games."
Bright spots for Everton included the performances of Ross Barkley and Deulofeu, who was one of three debutants along with John Stones and Joel Robles while Arouna Kone made a first start.
Deulofeu, on loan from Barcelona, was a constant menace out wide and scored a superb individual goal on the stroke of half-time while Barkley was dynamic in midfield.
But Stevenage, fresh from their first League One win of the season last weekend, proved resilient.
Boyhood Evertonian Greg Tansey - whose grandfather Jimmy Tansey played for the Toffees in the 1950s - almost snatched victory for the visitors when he forced Robles to tip over in the 90th minute.
Martinez said: "Stevenage were really well organised and gave an incredible effort.
"It was a great cup tie. I love this competition - the divisional status counts for very little.
"As a home team we had everything to lose. I was really pleased. I thought we managed the game well."