Spieth, the reigning PGA Tour Rookie of the Year, capped his round with birdie at the ninth hole on the par-71 Monterey Peninsula course to gain a piece of the lead.
Walker posted a birdie at the par-5 seventh on the par-72 Spyglass Hill course to tie him with Spieth at 9-under-par 134, one shot clear of the field.
The pair overcame chilly, windy conditions to put in solid rounds.
Hunter Mahan grabbed sole possession of third at minus-8 with a 68 at Spyglass.
Overnight leader Andrew Loupe had a tough second round, falling to a 1-over 73 at Pebble Beach for fourth place at minus-7.
Holding fifth one shot further back was Richard H. Lee (72).