The 30-year-old Englishman, who won his first professional tournament at this event 10 years ago, carded four birdies and two bogeys on Saturday, while a brilliant eagle at the 15th ended up leaving him at 12-under after three rounds.
But as he made his charge on 'moving day', there was disappointment as the well-placed Australian challenger Elvis Smylie, just three off the overnight lead, shot a woeful five-over 77 to slump back to one under in joint-46th place.
The Australian PGA champion's bad day reached its nadir with a quadruple-bogey eight at the 11th hole.
Fitzpatrick's performance so far at The Belfry has boosted his hopes of becoming one of Europe Ryder Cup team captain Luke Donald's picks.
The 2022 US Open champ holds a slender lead over Sweden's Alex Noren, who made five birdies and an eagle in a bogey-free 65 to climb to outright second.
England's Marco Penge also charged into contention after producing the round of the day, a course record-equalling bogey-free 63 that lifted the 27-year-old into a tie for third alongside Denmark's Nicolai Hojgaard (67).
Penge fired nine birdies, including three in succession to start his round, and back-to-back at the 10th and 11th, to sit two shots adrift of Fitzpatrick.
Should Hojgaard finish in a two-way tie for 29th place or better, he will secure the final automatic spot for Europe's Ryder Cup team ahead of Ireland's Shane Lowry.
Smylie's nightmare let in Jason Scrivener to nip in and become the leading Aussie for the week, his two-under 70 taking him to two under for the week, currently tied for 40th.
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