The Toffees can close the gap on third-placed Arsenal to just one point with victory at the Emirates Stadium on Tuesday night.
Saturdayâ€™s 2-0 victory over QPR has put Everton right back in the firing line for the coveted top-four spot Champions League qualification spot and are 10/3 with Paddy Power to beat the Gunners.
David Moyesâ€™ side are unbeaten in 11 of their 15 games on the road having won four and drawn seven and are 11/5 with the online firm in the draw no bet market to keep this run going.
Everton have scored in 12 of their 15 games on the road and are 4/11 to score against Arsenal or 7/5 to score the first goal against Arsene Wengerâ€™s side.
Moyes has praised his sideâ€™s battling qualities as they enter the final six games of the Barclays Premier League season having won four of their last five league games â€“that gives them a live chance of European football next season.
â€œThe players have got a real resilience and toughness to them. Because of that, we keep at it and the players know what is expected,â€ Moyes said.
“We played some good football against QPR and made quite a few chances but didnÂ´t convert them all.â€
Goalkeeper Tim Howard kept his third clean sheet in a row at Goodison Park and the visitors are 4/1 with Paddy Power to do the same on Tuesday night and 15/2 to win to nil against the North London side.
Midfielder Darron Gibson sent the Toffees on their way after his strike gave the home side the lead on 40 minutes while striker Victor Anichebe sealed the points in the 56th minute by flicking Sylvain Distinâ€™s header past Julio Cesar.
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Gibson and Anichebe are 18/1 and 10/1 respectively to get the first goal of the game with Paddy Power.
Anichebe has scored eight league goals this term and can be backed at 5/2 to score at anytime against the Gunners in his quest to hit double figures this season.
The visitors are 22/1 to repeat Saturdayâ€™s 2-0 scoreline against Arsenal who have never finished outside the top four during Wengerâ€™s near 17-year reign at the London club.
Kevin Mirallas made his seventh consecutive start for the Blues against Harry Redknappâ€™s side and his performances â€“ and three goals in four league games â€“ have been central to Evertonâ€™s resurgence.
The Belgian international is 5/1 to score first for his team or 16/5 to score at any time against an Arsenal side who have won their last four league games.