Poulter, whose only flaw on the day was an 11th-hole bogey, is one stroke ahead of Ashley Hall. Hall's 66 came despite a bogey and double bogey on the day.
Six golfers are tied for third at 4-under 67.
Poulter, playing the second nine of the Victoria Golf Course first Thursday, had a three-putt bogey on his second hole of the day. But he quickly returned to even with a birdie at No. 12.
He piled up five birdies in a six-hole span, starting with back-to-back birdies at 15 and 16 and three in a row over Nos. 18, 1 and 2. A closing birdie at the ninth hole gave him the lead.
Hall also opened on the second nine Thursday and was 8-under after 10 holes. That span included three straight birdies on Nos. 13-15 and a birdie-eagle-birdie string on 17, 18 and 1. However, he had a bogey at the fifth hole and a double bogey 6 at the eighth in dropping behind Poulter.
Swim Week Miami Beach 2014 [PHOTOS]