McGrane's fellow Irishman Peter Lawrie also carded a 64 on Saturday. That moved Lawrie into a share for second at 9-under-par 204. He was joined there by Jean-Francois Remesy (67) and Simon Dyson (66).
Australian Richard Green fired a course-record, 9-under 62 in the third round. That moved him from a tie for 62nd into a share of fifth. Green stands alongside Christian Cevaer and Soren Kjeldsen at minus-8.
Both the second and third rounds were completed on Saturday. The completion of the second round was pushed to Saturday morning after there were two weather delays totaling over four hours on Friday.
McGrane started the third round two strokes behind leader Ignacio Garrido. McGrane fell further back with a bogey on the first, but atoned for that mistake with a birdie on the par-4 fourth.
The 35-year-old then posted consecutive birdies from the sixth to get to minus-7. McGrane birdied the par-4 10th at Kennemer Golf & Country Club to join Lawrie atop the leaderboard.
McGrane, who is searching for his first tour win, parred the next four holes to fall one behind Lawrie.
He tied his countryman in the lead with a birdie on the 15th. McGrane grabbed first by himself when he pitched his third to two feet at the par-5 16th and kicked the putt in for birdie.
McGrane kept rolling with a birdie on 17. He made it four in a row to close out his day with a birdie at the last to end three clear of the field.
'Yeah it was very pleasing,' McGrane said of his round. 'I've played solid all week so far and my putting was good again today and I finished with four birdies...so it was a good finish and I was delighted with that.'
Lawrie flew up the leaderboard with five birdies in a six-hole span from the fifth. That gave him a share of the lead at minus-7 with Kjeldsen, Cevaer and Raymond Russell.
The Irishman birdied the 12th to take the lead, then was passed by Kjeldsen as he parred the next three. Lawrie joined Kjeldsen at minus-8 with a birdie on 16. He ended there with back-to-back pars to close his round.
'I had to hole two good pars putts on one and two, but after that I played lovely and putted lovely, which hasn't happened in a long time,' admitted Lawrie.
Remesy bogeyed the first, then notched consecutive birdies from the fifth. He remained at minus-6 as he ran off six pars in a row. The Frenchman birdied 13 and 14, then got to 9 under with a birdie at 17.
Dyson played the front nine in 2-under with birdies on one and seven. On the back nine, Dyson got to minus-seven with a birdie at 12. He drained back-to-back birdies from the 15th to gain a share of second.
Warren Abery and Alejandro Canizares each carded 66s in the third round to move into a tie for eighth at 7-under-par 206. They were joined there by Phillip Archer, who managed a 70 on Saturday.
Garrido tumbled into a tie for 17th at 5-under-par 208 after struggling to a 2-over 73.