Cabrera birdied the 18th to complete a flawless seven-under-par 65 shortly before lightning in the area forced the players from the course at Redstone Golf Club.
Pettersson was already safely in the clubhouse by that point after carding eight birdies and one bogey - on the 17th - in his opening round.
Pettersson, out of form coming into the tournament, admitted even he had been slightly surprised by his round.
Asked where it had come from, he said: "I don't know. I've missed last two cuts. I haven't played very well and changed my set-up a little bit and it seems to be working.
"I started off great with some birdies and it was a fun round. I really enjoyed it. I hit it well and played some putts."
American duo Jeff Maggert and Ricky Barnes were a shot further back after rounds of 66, while England's Lee Westwood also made a good start with a round of 68 to lie four under.
Westwood will make his 56th attempt to win a major at next week's US Masters, and for the fourth year running is warming up in Houston.
But the world number three did not stop off at Augusta National en route this time.
"I didn't think it was that necessary," the 38-year-old said.
"It's a nice place to go and soak up the atmosphere with nobody there and get some work done, but the course isn't really reflective of how it's going to be on Thursday morning next week.
"It changes so much in three days. I just decided not to this year and thought the extra couple of days at home would do me more good."
Westwood was runner-up to Mickelson at Augusta two years ago, while Cabrera claimed the coveted green jacket in 2009.
By the time the rain came, 51 players had finished their rounds, and organisers scheduled a start time of 7.30am (13.30 BST) for Friday.