The 39-year-old Swede, who is chasing his first European Tour victory since 2004, shot par on the front nine. He then birdied the 10th and holed another four birdies from the 12th.
McGrane, who started on the 10th tee, had five birdies before the turn. The Irishman added two more along with two bogeys on the final nine. He birdied the last for a share of the lead.
The trio of Andrew Butterfield of England, Estanislao Goya of Argentina and Carl Suneson of Spain each shot 68s.
Haeggman, who became the first Swede to represent Europe in the Ryder Cup in 1993, has revived his career this season after having to qualify for a spot on the tour.
Haeggmans last tour win was the Qatar Open in 2004.
The 13th and 14th holes feature 500-foot seaside cliffs on the Seve Ballesteros-designed course in Porto Santo. Its a small island off Madeira, a Portuguese archipelago in the Atlantic Ocean west of Morocco.