Preston North End 2 Oxford United 0 - Progress for PNE's Under-18s in the FA Youth Cup
Walker, recently back at PNE after a loan spell with Altrincham in the National League North, gave the Lilywhites a 20th minute lead from the penalty spot.
The Preston-born winger then doubled the advantage 10 minutes into the second half, meeting a cross from Lewis Coulton to flick the ball home.
It was a deserved win for North End who created a number of chances during the course of the evening,
However, Oxford had their moments too, PNE keeper Jimmy Corcoran pulling off three good saves.
North End now face Blackburn Rovers at Ewood Park in the fifth round.
The game had been switched to Deepdale after being postponed last Wednesday due to a waterlogged pitch at United's Kassam Stadium.
Oxford had the game's first clear-cut opportunity in ther 13th minute, Tyler Goodrham's corner from the left leading to a scramble in the box.
Callum Crook had two attempts to try and force it in before Corcoran grabbed it on the line.
North End took the lead in the 20th minute after Walker had been brought down in the box by United right-back Sam Johnson.
In the build-up Walker had twice made runs into the box and seen his path blocked, the third time seeing Johnson clip him.
Walker stepped-up to take the spot kick, cheekily chipping it over keeper Max Evans. There might have been a few words aimed in his direction had it gone wrong!
A couple of minutes later Walker was booked after an Oxford free-kick hit PNE's defensive wall - referee Robert Massey-Ellis deeming the winger had broken from the wall early.
When the second resulting free-kick was chipped into the box, Fabio Lopez's shot was tipped over the bar by Corcoran who did well to change position as the ball was in mid flight.
Walker's weaving run took him past three Oxford players in the 31st minute, Evans getting fingertips to his rising shot to take it over the bar.
Three minutes before the interval, Lewis Coulton's pass from the right-wing found Tyrhys Dolan, his ball inside collected by Jacob Holland-Wilkinson whose low shot was saved by Evans at the near post.
After the interval, Walker bent a free-kick from right on the edge of the box, wide of the far post, Lewis Coulton having been brought down.
The Lilywhites' youngsters doubled their lead in the 55th minute.
Walker's ball played in Holland-Wilkinson down the left hand side of the box, the striker's low shot across goal parried by Evans.
The ball came out to Coulton on the right-wing who returned it into the box, Walker nipping in ahead of the keeper to knock the ball into the net.
In the 64th minute North End counter-attacked from their own half, Holland-Wilkinson sweeping a pass to Dolan 35 yards out.
The PNE skipper advanced a few steps before trying his luck with a low shot which Evans got down to save.
At the other end, Oxford substitute Slavi Spasov was tripped by Lewis Earl two yards outside the box to win a free-kick.
Spasov dusted himself down to take the free-kick himself, his right-foot effort disappearing over the bar.
Another chance came Oxford's way in the 77th minute as Leon Chambers-Parillon cut inside along the byline and tried to squeeze a shot inside the near post, Corcoran blocking with his legs.
A late low shot on the turn from Spasov was touched round the post by Corcoran diving to his left, the keeper then tipping a header from the same player away in stoppage-time.
PNE: Corcoran, Dooley (Huddart 74), Williams, Earl, McFayden, Nolan, McManus, Coulton (Bennett 80), Dolan, Walker, Holland-Wilkinson. Subs (not used): Nicholson, Lewis, Leigh, Potts, Lombard.
Oxford: Evans, Johnson, Jones, Milton, Elechi, Sole, Chambers-Parillon, Smith (Ferguson 61), Goodrham (Edwards 90), Lopes, Crook (Spasov 61). Subs (not used): Gardner, Grant, Owens, Niemcycki.
Referee: Robert Massey-Ellis (West Midlands)