The Scot, winner of the 2004 PGA Championship, carded five birdies on the way out - including a hat-trick from the seventh - to move to eight under par.
The former Sir Henry Cotton Rookie of the Year had to chip in for birdie at the final hole of Qualifying School last year to regain his European Tour card, but the 36 year old's flying start put him just one behind the leading pair of Damien McGrane and Luke Goddard.
English Amateur Champion Goddard and Ireland's McGrane shared the overnight lead on eight under, but both advanced to nine under par in the early stages of their second rounds to hold off Drummond's charge.
Wales' Stuart Manley birdied the second to join Drummond on eight under, with England's John Parry and Norway's Eirik Tage Johansen a shot further back.
Johansen was the only one of the top five among the afternoon starters as he looks to secure a maiden top ten finish on The European Tour.