The Magpies secured their spot in the knock-out stages despite only earning a draw against the Portuguese outfit after Fidelis cancelled out Sylvain Marveaux's first-half strike
Sylvain Marveaux's netted his first goal for the club midway through the first half before substitute Fidelis earned a point for his side with an excellent individual effort.
Alan Pardew made two changes to the side that fell to a 2-1 defeat at Swansea, Gael Bigirimana coming in for Cheikh Tiote and Papiss Cisse replacing Demba Ba up front.
Chances were sparse in the early stages as both sides were reduced to efforts from long range as they struggled to establish a foothold in the contest. However, the Magpies opened the scoring with their first real opportunity as Marveaux latched onto a wonderful through ball from Hatem Ben Arfa before accelerating and slotting past Romain Salin at the near post.
Newcastle continued to dominate proceedings following the goal, and Pardew's men had a goal ruled out 10 minutes before the half when Cisse pounced on a rebound after Bigirimana had forced a strong save from Salin, only to see his effort ruled out for offside.
The Tynesiders suffered a blow in the build-up to that chance however, as Hatem Ben Arfa was forced to limp from the field with an apparent hamstring injury.
Ba came on in Ben Arfa's stead, but that change did nothing to alter the flow of the contest, which the home side were able to control with relative ease as the visitors offered little as an attacking force.
Cisse was replaced by Romain Amalfitano early in the second half, but it was Maritimo who had the first chance of the period, as Danilo Dias forced Tim Krul to tip over the bar with a fierce long-distance drive.
Dias was at the hub of all the positive play from the visitors and he fashioned another chance for the Portuguese side as his cross was met by Sami, who headed wide from point-blank range.
Newcastle were more of a subdued threat as the game wore on, but they did go close to adding a second midway through the second half when Sammy Ameobi flicked the ball narrowly wide of the post from an in-swinging free-kick.
Maritimo refused to give up the fight despite harbouring no realistic hopes of qualification, and they forced another good stop from Krul when Ruben Ferreira hit a powerful shot from the edge of the area.
Ba was denied two opportunities to kill the game off, however minutes later the men from Madeira grabbed the equaliser their efforts perhaps merited as Brazilian striker Fidelis surged into the box before directing a low shot underneath Krul and into the bottom corner.
Fidelis soon had the ball in the net again, but this time his strike was chalked for offside, much to the relief of the watching Newcastle faithful.
However, despite the best efforts the visitors of the Brazilian - who fired a volley wide from close range in the dying embers of injury-time - the vistiors were unable to find the goal that would have earned them an stunning victory, and Pardew's men were able to hold out and secure a point that keeps their hopes of winning the tournament very much alive.