Mickelson's bogey-free round allowed him to complete 54 holes at 13-under 203, tying him with Verplank, who carded a 5-under 67 Saturday.
Mickelson matched the course record for the Tournament Course at Redstone Golf Club. It was previously set by Adam Scott and Johnson Wagner in 2008 and then tied by Jimmy Walker in Thursday's first round.
Mickelson in 2006 won the Houston event and then followed it with a victory the next week at the Masters.
Aaron Baddeley (66) and second-round leader Chris Kirk (69) finished tied for third one stroke off the lead at minus-12.
David Hearn (66) and Anthony Kim (69) were in fifth place at minus-11.