The Toffees are eight points behind Arsenal and could keep up their outside push for a Champions League place when they face the Magpies.
The Merseysiders are fifth in the table and still harbor hopes of securing a place in next season's Champions League. They cut the gap to fourth-place Arsenal to eight points with a pulsating 3-2 home victory over Swansea City on Saturday as Arsene Wenger's men slumped to a 6-0 defeat at Chelsea.
The Toffees also have a game in hand over the Gunners as they prepare to travel to Newcastle on Tuesday and the Spaniard is eager to ensure that his players do not waste the opportunity in front of them.
MORE: Chicharito out of Mexico's XI | Madrid surrenders title supremacy
"We're in a very, very good moment," Martinez told reporters after beating Swansea. "The players are fresh, looking forward to every game. We've got nine games to go and we need to make sure that we take advantage of every single point that we can get."
The stadium ban handed out to boss Alan Pardew following his headbutt on Hull City's David Meyler did little to hamper them on Saturday as they left it late to beat Crystal Palace 1-0 at St. James's Park.
Papiss Cisse's injury-time strike gave them all three points to move them up to eighth, with assistant John Carver masterminding things from the dugout in Pardew's absence. That strike marked a first goal in more than two months for the Senegal forward and captain Fabricio Coloccini hopes that he can now kick on from here.
"We are all so happy for him because strikers live to score and he has been a bit unlucky in the last few games," the defender told Newcastle's official website. "He had a few chances [against Palace], which their goalkeeper saved, and then missed one from Mapou [Yanga-Mbwia's] cross but he never gave up and hopefully this gives him a lot of confidence."
Ahead of facing Everton, Cisse and his fellow strikers will also be heartened by the fact that games between these two sides have generally delivered plenty of excitement, with all of the last six encounters featuring three goals or more. The pair's most recent encounter ended in a 3-2 win for Everton at Goodison Park back in September.
The absence of injured top scorer Loic Remy, who will miss out again with a calf injury, could hamper Newcastle and they will also be missing fullback Mathieu Debuchy with a groin ailment. Davide Santon remains a doubt due to a knee problem, while Gabriel Obertan is also out with a similar concern.
For Everton, Phil Jagielka is doubtful with a hamstring injury, while a knee problem could keep midfielder Steven Pienaar out of action for the third consecutive game.
The visitors have no other new injury concerns, with long-term absentees Lacina Traore (hamstring), Bryan Oviedo (broken leg) and Arouna Kone and Darron Gibson (both knee) all still unavailable.