Allen bested the former mark of 11-under 61 at the Old Course in Baco Raton, set during last year's event by defending champion Rocco Mediate.
Allen finished 18 holes with a three-stroke lead while seeking his sixth Champions Tour title.
Finishing alone in second place was tour rookie Scott Dunlap with a 9-under 63.
2011 champion Tom Lehman carded a 7-under 65 to share third place with Wes Short Jr. and Chien Soon Lu.
2014: NFL Cheerleaders [PHOTOS]
Michael Sam cut from the Dallas Cowboys