Brooks shot a superb 64 in the third round to take the clubhouse lead, but Garcia's 68 put him ahead of the Englishman.
The Spaniard celebrated being given honorary life membership of the European Tour on Friday as he birdied the second and third, delighting his fans in Cadiz.
Overnight leader Joost Luiten of the Netherlands, who picked up the third albatross in the tournament's history on Friday, is two shots off the pace after shooting a 71 on an inconsistent day.
(Reporting by Rik Sharma; Editing by Christian Radnedge)
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