Stricker, ranked third in the world, chipped in from 20 yards off the green for a birdie at the par-4 18th and shot a 6-under 65 in rainy conditions at the Riviera Country Club. He completed 36 holes in 10-under 132.
Johnson aced the par-3 fourth and was also at 10-under with two holes to play when the action was suspended because of darkness.
Rain fell off and on all day and a blustery wind added to the difficult playing conditions.
"It was pretty miserable out there today," said Stricker. "It never really let up."
There were still 40 players on the course when it became too dark to play.
They were scheduled to return at 7:30 a.m. local time and tournament officials hoped to be able to complete the third round on Saturday.
Andres Romero was alone in third place at 7-under through 15 holes.
At 6-under 136 were Justin Rose, Tim Wilkinson and Kevin Stadler. Anthony Kim, Ricky Barnes and Steve Marino were all at 137.
Phil Mickelson climbed his way back into the tournament with a 5-under 66. He moved up 72 spots on the leaderboard and was at 4-under 138.
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