The Italian followed up his 65 from the opening day with a five-under-par round that included six birdies - four of which coming on the front nine - and just the one bogey.
That left the 35-year-old, who has only had his European Tour card seven days after finishing third at the Qualifying School at PGA Golf Catalunya last week, on 12 under for the tournament and with a one-shot lead over the chasing pack.
Morten Orum Madsen was his nearest challenger after an impressive 66 on Friday left the Dane 11 under. It would have been even better for Madsen put for a bogey four on the penultimate hole - his only dropped shot of the day.
South African Jbe Kruger was third on nine under after a 70, with English duo Tom Lewis (68) and Matthew Nixon - the overnight leader - one shot further back on eight under.
Nixon eagled the penultimate hole on Thursday to claim a one-shot lead over Crespi and Kruger at the end of day one, but he was unable to build on that start as he carded a level-par 72 for the second day.
Nixon picked up birdies on the eighth, 13th and 15th, but a bogey on the first and a double-bogey on the par-four 10th pegged him back.
Of the later starters, former Masters champion Charl Schwartzel was powering up the leaderboard after carding successive birdies on the opening three holes, leaving him on eight under. Schwartzel has yet to drop a shot in the tournament.
His South African compatriot Christiaan Basson, meanwhile, was level par after four after staring with a 66 on the first day.