Eddie Howe's are in third place ahead of Thursday's home clash with Brighton & Hove Albion, ahead of Manchester United on goal difference, and one point ahead of fifth-placed Liverpool who are mounting a late charge.
Newcastle and United both have three games to play, compared to Liverpool's two, but with Jurgen Klopp's rejuvenated team on a seven-match winning streak, both are anxiously looking over their shoulders.
Victory over Brighton would settle the nerves after picking up only one point from their last two games.
Although, Brighton are chasing a European spot for the first time in their history and will be full of confidence after demolishing Arsenal's title dream on Sunday with a 3-0 away win.
Former Bournemouth boss Howe, who has turned Saudi-owned Newcastle from relegation contenders into top-four challengers since taking charge 18 months ago, knows getting across the line might be the toughest part of the season.
"I'm well aware of the importance of every game. We're running out of games, there's three games left in the competition for top four," he told reporters.
"This will be the hardest bit, we need everyone to pull together to achieve it. When you're playing the important games that's what you're in it for.
"Every big experience I've had as a player or manager, the day or night before your senses are heightened. We've tried this week to take any pressure off and enjoy our football."
Newcastle have not played in the Champions League for two decades and to miss out now after such an impressive campaign would be a bitter pill to swallow.
Howe said cool heads will be required against a sixth-placed Brighton side who ruthlessly picked apart Arsenal on Sunday.
"One of the things I've always used in pressured situations for the players is to keep things very simple, clear and to not over-complicate things," he said.
"I think it's going to be a really tough assignment for us but one, at home, that we're not fearful of and hopefully we'll take a big step forward."
Howe confirmed Newcastle will be without injured Sean Longstaff while Jacob Murphy is also a doubtful starter.
After Brighton, Newcastle host relegation-threatened Leicester City before finishing up at Chelsea.
