Rose also was a co-leader with Paul Broadhurst after Thursday's first round.
In Friday's second, he shot 2-under-par 70 to maintain his spot at the top of the leader-board, while Cabrera shot 8-under 66.
Their 36-hole total is 8-under 136.
Three late birdies helped.
"The finish turned the day from a bad day into a good day," Rose said. "That was a great way to finish and salvage the day. It's a great start, and it's nice to be in the hunt going into the weekend."
Ross Fisher (67) is alone in third place at 7-under 137.
Broadhurst (72) is among six players tied for fifth at 6-under 138.
One of the others in sixth place is Padraig Harrington (69), who won last week's Irish Open.
Swim Week Miami Beach 2014 [PHOTOS]