Johnson's 8-iron from 152 yards landed between the pin and the famous bunker in the middle of the green at No. 6, spinning back into the cup for an ace that put him in the lead for most of the afternoon. He had two holes left when play was halted by darkness.
Stricker, playing in a morning rain that never relented, chipped in for birdie on the 18th and nearly made an ace on No. 4 when his hybrid from 230 yards lipped out. He shot a 6-under 65 and had the clubhouse lead.
"I'm very happy to be done with the round, to tell you the truth," said Stricker, who was at 10-under 132. "It was pretty miserable out there today."
Johnson, also 10 under after making his lone bogey on the 15th, was to return Saturday to face the par-5 17th and the 473-yard closing hole at Riviera, which was playing so long in the cold and rain that some players barely reached the green with a 3-wood.
Johnson and Stricker were three shots clear of Andres Romero, who had three holes remaining. Forty-one players failed to finish the second round.
Phil Mickelson, trying to become the first player to win three straight years at Riviera, had a 66 and was at 4-under 138.
Darkness came early because of the gray clouds, and completing the second round in such conditions was impossible. Players had to spend extra time on every shot to wipe off the grips of their clubs and the brims of their hats. Late in the day, the maintenance crew had to roll water off the soaked tee boxes.
That made the performance of Stricker and Johnson even more remarkable.
"Dustin Johnson is 11 under," Paul Goydos said in amazement as he walked off the 11th tee. "That's like being 47 under through three rounds at the Hope."
Ahead of him was Stephen Ames, bundled in rain gear and making light of the gloomy conditions.
"I don't play golf for money. I play golf for fun," Ames said, breaking into a smile. "And this is not fun."
Johnson, who opened with a 64 for a one-shot lead, caught the brunt of the weather. Temperatures dipped into the 50s, and with the steady rain and soaked conditions, some players couldn't carry their tee shots much more than 225 yards.
"I don't like it, but do I mind playing in it? No," Johnson said. "Everyone has got to play in it. Hitting it a long way helps, too, because the course is by far the longest I've ever seen this course play."
Stricker chipped in from 60 feet for birdie on the 18th, after hitting a driver and a 3-wood to the edge of the green. Most players were hitting an 8-iron or 9-iron in sunny conditions on Thursday. Johnson usually can reach the 583-yard 11th hole with a big drive and a 3-iron. He hit a big drive Friday, then crushed a 3-wood and still had 100 yards left.
Johnson hit a punch wedge to 6 feet and missed the birdie putt. What kept him atop the leaderboard were the par putts he made around that, from a 15-footer on No. 10 to an 18-footer on the 12th, and a 6-foot par save on the 13th.
They were important, just not nearly as thrilling as No. 6. Johnson is not one to get excited, and explained his ace thusly: "Probably my best shot of the day. Hit 8-iron and made it."
If anyone can handle the rain, leave it to Johnson. He won at Pebble Beach last year when the tournament was cut to 54 holes because of rain, and at Turning Stone in 2008, which was slowed by rain early in the tournament.
The forecast was for more rain overnight, and throughout Saturday.