England veteran Casey shot an impressive 67 at the hard Spyglass Hill course to climb to 15-under the card, earning a three-shot lead over Phil Mickelson (70).
Mickelson, a four-time victor of the event, teed off on the 10th and raced to six under for his round with six birdies in his first 14 holes.
Three later became four when Casey completed a bogey-free 64 at Monterey Peninsula, the Englishman flying up the leaderboard when he made four birdies and one eagle in a sparkling six-hole run on the back nine, although he managed only one more gain at the sixth as conditions deteriorated.
Mickelson was part of the celebrity rotation at Pebble Beach and put on a show on the back nine, stuffing a wedge to 3 feet on No. 13, and following with a 4-iron to 4 feet on the par-5 14th hole for eagle.
Case in point, this shot on Pebble Beach's fourth hole during Saturday's third round.
Mickelson, among the leaders starting the round, was even for the day through nine after three bogeys and three birdies. "It was very hard but I was able to come back when it cleared up".
"I actually thought it was a successful round", said Mickelson, who said the sometimes-heavy showers made the going tough at times.
The four-time champion picked up further shots at 17 and 18 to turn in 32, and after missing out on another at the par-five first, he atoned with a pair of twos at the third and fifth before three wayward tee shots led to bogeys on each of the next three holes.
"I just have to play a good solid round", Mickelson said. Casey is an ambassador for UNICEF and has the logo on his golf bag, which he displayed on an Instagram post to confirm he was not playing. "He's going to be tough to catch".
"I stand firm on what I said", Casey said.
Jordan Spieth, who was tied for the lead through 16 holes when rain halted the second round on Friday, returned with a late bogey to start the third round one off the pace.