MacIntyre had two bogies and two birdies on his front nine as he struggled to get the ball close to the hole.
He then dropped two shots in quick succession at the 13th and 14th holes before a birdie at the par four 16th gave him some hope of victory heading into his final 18 holes.
Jack MacDonald, the only other Scot in the field, is on four over par and in a tie for 74th position in what is only his second major championship.
MacIntyre begins his final round at 12:05 BST on Sunday alongside American Cameron Young, with MacDonald out at 08:00 alongside another American, Ben Griffin.