The closest to a fright for Walker came in the 28th minute when Sol Campbell won some Brownie points by dispossessing the flying Andrei Kanchelskis, only to send his back-pass straight to Daniel Amokachi. Fortunately the Nigerian striker found the shooting angle too tight and could only hit the angle of the post and crossbar.
That evened matters somewhat as Chris Armstrong had rattled Neville Southall's crossbar as early as the fourth minute, when Ruel Fox set up the chance. Anders Limpar threatened all sorts of danger on Everton's left, but only once did he force Walker into a save.
The entertaining rhythm both sides had maintained was interrupted just before half-time, when Armstrong and Everton's Craig Short were led off the field bleeding from head wounds. Armstrong came back but the Everton defender needed nine stitches and was replaced by Andy Hinchcliffe.
Except for a superb through-ball from Teddy Sheringham, which gave Armstrong a chance to prove Southall's reflexes are still in perfect working order, Spurs had found Dave Watson and Short almost impassable. Fox occasionally caused minor havoc wide on the right wing, but the route through the middle was blocked.
With Kanchelskis finding less and less space in the second half Everton's menace diminished, although Colin Calderwood was always ill at ease with the rumbustious Amokachi. But the astute perception and intervention of the Spurs captain Gary Mabbutt helped steady defensive nerves.
The stalemate was almost broken in the 60th minute, when a Sheringham free-kick on the edge of the box was deflected wickedly beyond Southall only to rebound to safety off Hinchcliffe.
Four minutes from the end a gigantic clearance from Walker was missed by Watson for Armstrong to poke the ball beyond the advancing Southall. But Matthew Jackson had recovered his wits sufficiently to keep the scoresheet blank, between two evenly matched sides both lacking the touch that might have unlocked the game. Everton, at least, could plead that their candidate for the role was missing simply because he's been locked up.
The Everton manager Joe Royle admitted afterwards that Newcastle and Manchester United are still a few steps ahead of the rest of the Premier League. Both Everton and Spurs seem a few players short of mounting real and purposeful challenges.