The game was largely one to forget for both sides, as Newcastle failed to mark Rafa Benitez's 100th game in charge of the club with a positive result.
Everton dominated the ball early on, with Cenk Tosun slicing an early effort wide of the far post.
The hosts clearly looked to use the pace of their wingers to get in behind the visiting full-backs, with Mogan Schneiderlin looking to release Walcott and fellow wideman Yannick Bolasie at every opportunity, but the tactic failed to bear fruit in a drab opening 45.
Both sides spurned decent chances to open the scoring just before the break as Phil Jagielka volleyed over on the stretch after meeting Michael Keane's knock-down six yards out, before Jordan Pickford in the home goal saw his kick charged down by Kenedy, with Ayoze Perez unable to play the simple pass that would have set Islam Slimani through on goal on his first Newcastle start.
With that the two sides went in level at the break, but within six minutes of the resart, Everton found the breakthrough.
Yannick Bolasie was afforded space down the right and he crossed for Walcott at the far post. The England man's touch was poor but the ball ricocheted back into his path off DeAndre Yedlin, allowing him to step inside and lift the ball past Martin Dubravka and into the roof of the net to open the scoring.
Newcastle improved from that point on and could have levelled when substitute Dwight Gayle volleyed over after Jamaal Lascelles had flicked Jonjo Shelvey's right-wing corner into his path just after his introduction.
Matt Ritchie later curled a free-kick narrowly over but Newcastle were unable to find a way back into the game as they slumped to defeat.
The result sees Everton leapfrog Leicester into eighth, whilst Newcastle remain 10th.
23 April 2018