One day after Scot Paul Lawrie and Australian Wade Ormsby had fired nine-under-par 61s, Fitzpatrick went one better with a 60.
The 21-year-old had a birdie putt at the last to go round in 59 but left his effort agonisingly short.
"I was just trying to get the 'read' right... in fact I was thinking so much about the line I forgot about the pace of it," Fitzpatrick told reporters after his nine-under total of 131 left him three strokes behind leader Soren Kjeldsen of Denmark.
"It was a bit disappointing to leave it short. But it's been a great day and I can't have any complaints about a 60."
Kjeldsen matched his opening 64 to lead by one stroke from Ormsby (68) and England's David Horsey (66).
Eight-times major winner Tom Watson, 66, carded a 68 for 137 as the veteran American become the second oldest player in European Tour history to make the cut.
(Writing by Tony Jimenez,; Editing by Pritha Sarkar)
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