He found 10 of 14 fairways and 14 of 18 greens in regulation but missed several short birdie putts to post an even-par 72 and a nine under total.
England veteran Casey shot an impressive 67 at the difficult Spyglass Hill course to climb to 15-under the card, earning a three-shot lead over Phil Mickelson (70).
Former US Open winner Lucas Glover (70) and fellow American Scott Piercy (69) share third at 11 under.
With heavy rain and winds up to 25km/h predicted for Sunday, local time, Day says he’s still a good chance to steal victory.
«I don’t have to do anything crazy tomorrow to win the tournament, I would say,» Day said.
He is also inspired by an impressive record at the event, posting five top-six results from nine previous appearances.
Helping his quest is the fact Casey is not a prolific frontrunner, winning just one PGA Tour event from the four times he has held a 54-hole lead.
«Conditions are going to be tough,» Day said.
«I know I can get out early and post a number, something that’s significantly in the 60s, and put a little bit of pressure on those guys.»
Searching for his fifth PGA Tour victory at Pebble Beach, Mickelson welcomed the brutal forecast.
«I don’t mind if it gets really rough … to have my best chance, the weather would have to come in,» he said.
Curtis Luck (73) was next best of the Australians at five under, while countrymen Cameron Davis (72) and Matt Jones made the three-under cut on the number.
Adam Scott bogeyed the 18th for a 71, finishing at two under alongside John Senden (69).
Given they finished between 60th and 71st, Scott and Senden made the event’s 54-hole cut but not the final round.
Ryan Ruffels (one under) Aaron Baddeley (one over) and Rod Pampling (nine over) all missed the cut.