England's Stuart Little posted a 3-under 67 to share fourth place with Michael Jonzon of Sweden.
McGrane picked up his first birdie of the day at the par-3 second and added another at the par-5 sixth. He then birdied the eighth but dropped a shot at the ninth to make the turn at minus-2 at Pula Golf Club.
The Irishman recovered quickly on the inward half with a birdie at the 11th and holed his approach to the par-4 14th for an eagle.
McGrane, whose best finish this year on the European Tour was a tie for fourth at the Aa St. Omer Open, kept the run going with back-to-back birdies from the 15th to reach 7 under and managed a two-stroke advantage despite a bogey at the last.
'There's no pressure on me,' said McGrane, who is currently 142nd on the Order of Merit and needs a strong finish this year to secure his card for 2004. 'This game is hard enough without putting pressure on yourself when you are out there.'
Olazabal, who tied for 10th at this year's Canarias Open de Espana following a solid performance at The Masters, tallied a birdie at the third and ran off consecutive birdies starting at the par-3 ninth to move to 3 under.
The two-time Masters champion added a birdie at the par-4 15th en route to a bogey-free round of 68.
'It was a tough day because of the wind coming in different directions, which makes it difficult to choose the right club,' said Olazabal. 'I had good and bad shots but managed not to get into trouble. I haven't had such a good round for a long time and that gives me a lot of confidence.'
Maarten Lafeber, who earned his first career victory on the European Tour last week at the Dutch Open, collected five birdies and three bogeys for a round of 68.
'My score was pretty good considering I didn't hit the ball very well,' said Lafeber. 'I finished with a bogey that was disappointing but I'm happy with the way I played.'
Lafeber was joined by Marcel Siem, Matthew Blackey, Paul Broadhurst, Jose Manuel Carriles, Santiago Luna, Gustavo Rojas, Scott Drummond, Benn Barham, Henrik Stenson, Martin Lemesurier and Sion E. Bebb in a tie for sixth at 2 under par.
Lee Westwood, who has two victories to his name so far in 2003, posted a 2-over-par 72 to finish in a group that featured Spain's Miguel Angel Jimenez.