After a delay of more than 3 hours while storms deposited an inch of rain on the course, action was stopped for the day. The first round will resume early Friday.
Cabrera has won only twice on the PGA Tour and both those victories came in major championships -- the 2007 U.S. Open and the 2009 Masters. He put together a bogey-free round Thursday at the Redstone Golf Club.
Cabrera has missed the cut in four of his previous five starts this season and has had a sub-par score in just four of his 13 rounds.
Keegan Bradley, James Driscoll and rookie Bud Cauley were all at 67.
Defending champion Phil Mickelson had played only three holes before the rains came and he stood at 1-under.
This is the last tour event prior to the playing of the Masters, the year's first major tournament.