Allen is a PGA Tour regular who hasn't won since 1998 on the Nationwide Tour and is playing in his first Champions Tour event. He completed 54 holes at 3-under 207.
Former Masters champion Larry Mize (71) stumbled with three bogeys and a double-bogey on the back nine but wound up in fourth place at 209 with Gil Morgan (70) and Tim Simpson (68).
Second-round leader Ross Drummond (76) dropped him into a share of 16th at 212.
Swim Week Miami Beach 2014 [PHOTOS]