A first victory in four for the Toffees lifts them above Leicester City and into eighth, four points ahead of Newcastle who had climbed to 10th with four straight wins.
Chances were few and far between in the first half but one did fall the way of Cenk Tosun within three minutes, only for the Turkish striker to slice an ugly left-footed volley wide.
Despite having 68% possession before the break, it took another 30 minutes for Everton to fashion their next opportunity as Phil Jagielka poked wide on the stretch following Michael Keane's knockdown.
Newcastle immediately went up the other end and squandered a glorious opening of their own as Ayoze Perez overhit a simple pass to Islam Slimani, which would have sent the Algerian through one-on-one with Jordan Pickford, whose scuffed clearance had seemed to have gift-wrapped United a certain goal.
The game badly needed a goal and it arrived in the 51st minute, when Walcott kept his cool to escape a couple of Newcastle challenges and thrash a shot into the top corner, after DeAndre Yedlin had failed to clear his lines at the back post from Yannick Bolasie's cross.
Perez, who had three goals in three games prior to kickoff, had lacked the same composure moments earlier when he stabbed wide with his left foot from 12 yards out. The Spaniard did find the target with a header on 72 minutes, but it was straight down the throat of Pickford.
Rafael Benitez had dared to change a winning formula by dropping Dwight Gayle for Slimani, and he later called for the former Crystal Palace man from the bench after the Algerian had failed to make an impression.
Gayle immediately had a chance to equalise when he hooked over the crossbar from six yards out, albeit under pressure from several defenders, after Jamaal Lascelles had won a near-post flick-on from a corner.
While Newcastle were not exactly banging on the door for a late equaliser, Everton had to endure a couple of close shaves, firstly when an 87th-minute penalty could have been given for handball against Jagielka.
Seamus Coleman also had to rescue the hosts with a headed clearance off the line seven minutes into stoppage time, as Everton saw out a 10th home league win of the season and fifth in a row versus the Magpies.
EVERTON (4-3-3): Pickford; Coleman, Keane, Jagielka, Baines; Gueye, Schneiderlin (Davies, 52'), Rooney; Walcott, Bolasie (Calvert-Lewin, 59'), Tosun (Niasse, 85')
NEWCASTLE (4-4-2): Dubravka; Yedlin, Lascelles, Lejeune, Dummett; Ritchie (Murphy, 79'), Shelvey (Merino, 83'), Diame, Kenedy; Perez, Slimani (Gayle, 63')