Moments later, Everton went in front when Yannick Bolasie whipped in a deep cross from the right and former Arsenal winger Walcott brought the ball down before taking his time to fire home the victor and lift them to 45 points from 35 games.
Everton are now in ninth place, just one point ahead of Newcastle, with the Magpies also possessing a game in hand.
Everton's head of engagement, Scott McLeod, said: "The most important thing for everybody at the club is that we have had the opportunity, through this wonderful technology and the work with No Isolation and WellChild, to do something incredible for an inspirational young Evertonian".
And the Toffees boss is determined to have a strong end to the campaign and finish as high as possible, with Leicester City the only side Everton could realistically pass.
"What was wrong with our style today?"
The Toffees got off to an encouraging start, with Cenk Tuson firing just wide from 12-yards out after some good work by Walcott. "We completely dominated the game", Allardyce said on Sky Sports.
The 63-year-old lasted just eight months at St James' Park as fans quickly turned against him but since then he has gone on to take charge of Blackburn, West Ham, Sunderland, England and Crystal Palace before arriving at Goodison Park in November as Ronald Koeman's successor. You can knock some of the passing that goes astray buy you can't knock me for that, I don't pass the ball.
Newcastle are virtually assured of survival and manager Rafa Benitez said they could have gained more from the game with a little extra finesse. "To stay in the Premier League was the target and we are really clear with that". "If you see Huddersfield, if you see Brighton and ourselves, we are organised, so we have better balance between attack and defence and that is the reason why maybe the three of us can stay in the Premier League".
Keys helps USA book Czech Fed Cup final
The Czechs are into their sixth Fed Cup final in the last eight years, winning in 2011-12 and 2014-16. I knew I had to start very strong today and continue that throughout the game.
Shift Nanar refinery to Gujarat, Shiv Sena dares BJP
Meanwhile, another Sena leader claimed that Uddhav Thackeray may suggest that the project be shifted to Vidarbha region. Thackeray alleged that the "land mafia" had been buying land in Nanar following the notification.