Narat was about to play the 13th hole when play was suspended a third straight day at the weather-plagued, $5 million event.
The 25-year-old Bangkok native used three birdies and an eagle to compile a total of nine-under-par through the 12 holes he was able to play.
England's Simon Dyson, first-round leader Lam Chih Bing, a local pro from Singapore, and Denmark's Thomas Bjorn were tied for second at 7-under.
World No. 5 Padraig Harrington of Northern Ireland, the winner at this season's British Open and the PGA Championship, held the clubhouse lead at 5-under after shooting 5-under 66 Saturday.
Elsewhere, world No. 3 Phil Mickelson was 4-under through 14, South Africa's Ernie Els 1-over through 11, Rory McIlroy of Northern Ireland was 1-under through 11, and India's Jeev Milkha Singh was 4-under through 14 holes.
Swim Week Miami Beach 2014 [PHOTOS]