Armour, making only his second start on the Champions Tour, carded an 8-under 64 while Simpson finished the second round with a 7-under 65.
After faltering on the front nine, Armour struck a great seven-iron on the par-3 16th that rolled 5 feet from the stick, and the following birdie putt put him alone in front. He nearly missed an eagle on the par-5 18th.
Simpson birdied the 17th and eagled the close par-5 18th hole, chipping in to finish his last two holes in 3-under and grab a share of the lead.
Swim Week Miami Beach 2014 [PHOTOS]