The start of the day's play was delayed by an hour for rain and stopped again for two hours as a hailstorm hit the California course.
Mickelson is now top of the leaderboard on 18-under with two holes left to play, while Casey is on 15-under with three holes left.
"We've got two tough holes left and I don't want to jump the gun and get past that", Mickelson said. "But I wanted to try to finish tonight because I'm playing well".
It is Mickelson and Casey now battling to win the tournament, while Scott Stallings also has an outside chance.
The 48-year-old, five-time major victor took home his second tournament in the last two years after not having won since 2013.
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The Argentine appeared to shout "f*** off" at United fans, moments after PSG took the lead at Old Trafford on Tuesday. I only had problems with the coach [Louis van Gaal] here".
Those two will still be rivals when they reach the seniors circuit and I think there's an element of "I'll show you I can still do it" about Mickelson's own recent good form.
Mickelson briefly went three ahead after converting from eight feet at the 13th, before picking up a sixth birdie of the day at the par-five next to match Casey's 15-footer from the fringe.
Mickelson sits at -18 for the tournament, with three holes to play.
Third-round leader Paul Casey, who mixed two bogeys with two birdies, was at 15 under with three holes remaining, tied with Scott Stallings who finished with a 66.
"Every time I get here I have such feelings of gratitude that all that this place has done for my family, starting with my grandfather", he said.
"Here I'm trying to hit the ball as far as I can, not anxious too much about the rough, balls plugging and we're able to clean it".
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Phil Mickelson has won the weather-affected AT&T Pebble Beach Pro Am and [1000.0] shot, David Law, has won the ISPS Handa Vic Open.
Law trailed Ormsby by fully five strokes after his penalty and he still trailed by three with just three to play but he birdied the par four 16th, parred the tricky par three 17th and then did this with his second to the par five 18th!
"I take a lot from this", Casey said.
He has won five majors - the Masters (2004, 2006, 2010), PGA Championship (2005) and British Open (2013).
Casey called Mickelson's effort "a phenomenal round of golf" but added: "It's not over yet".
Casey blinked first with a bogey on the 11th hole, and another on the par-3 12th when his tee shot came up short and into the bunker.
OPEC Cuts Oil Production by 800,000 Barrels a Day in January
The country's average heavy crude price was also reported to be $56.29 since beginning of 2019 up to the report's publishing day. WTI futures hit a high of $53.70 per barrel before receding slightly to $53.54 per barrel, a 0.83 percent rise, as of 2:04 p.m.