The dream is still alive as the Toffees battled back from a goal down against Sunderland last weekend to win 2-1 and confirm their top-four credentials.
Everton now hit the road for Saturdayâ€™s clash against Reading in confident mood after halting a run of four successive draws when accounting for Martin Oâ€™Neillâ€™s side last weekend.
David Moyesâ€™ side have now conceded the first goal in all their six matches but have battled back to win two, draw three and lose just once.
Marouane Fellaini has taken over at the top of the clubâ€™s leading-scorer list in the Premier League with six goals as his 77th-minute strike levelled the game before Nikica Jelavic made the points safe two minutes later.
Everton are 7/1 to win by the same scoreline against Brian McDermottâ€™s side who have yet to register a win in the Premier League but have been knocking on the door recently and kept their first clean sheet against Norwich last weekend.
Leon Osman will be looking to cap a special week for him as he was at the heart of the England midfield in the 4-2 loss to Sweden.
Manager Moyes was full of praise for the 31-year-old who played the full 90 minutes on Wednesday on the back of some impressive performances in Evertonâ€™s solid start to the campaign.
â€œHe is a determined, committed and a really good footballer. We have played him in three or four different positions and because of the level of football intelligence he has got, he is able to do those jobs to the best of his ability,â€ he said.
Osman is 4/1 to score at anytime against Reading over the 90 minutes to add to his 45 goals in 313 appearances for the club.
Everton won 2-0 at the Madejski Stadium in 2006 and a repeat of that is 17/2 with Paddy Power.
Saturdayâ€™s clash is the Toffeesâ€™ seventh game on the road this season and they have only lost once to date (at West Brom) scoring 12 and conceding eight in the process. That defeat at the Hawthorns is also the Toffees only loss in 11 games so far this season.