A handful of second rounds were concluded early on following Friday's early finish due to a band of storms, before the Argentinian opened up a two-shot lead over Bill Haas.
Romero was 10 under par and four under for the third round through the first eight holes, while American Haas also climbed up the leaderboard following six birdies and two bogeys on the outward nine.
Roberto Castro, who had shared top spot with joint overnight leader Jordan Spieth, had slipped down to a four-way tie for fourth after eight holes due to a bogey on the second and a double-bogey at the third, before back-to-back birdies on the seventh and eighth helped to contain the damage.
Spieth also tied for fourth along with Americans James Driscoll and Jason Kokrak on six under, while Belgium's Nicolas Colsaerts picked up two shots to be seven under and move into third.
American Tom Gillis surged 22 places into a share of eighth spot on five under through 16 holes, alongside South Korea's Dong-hwan Lee.