Pole Adrian Meronk, who requires a tie for second or better in the last qualifying event to give himself a chance of leapfrogging MacIntyre, had moved into a share of the lead with Fitzpatrick on 12-under-par after covering the opening 15 holes at Crans-sur-Sierre in a blistering nine-under.
But a bogey-double bogey finish - he lost his ball off the tee at the 18th - saw him slip into fifth alongside potential Ryder Cup pick Ludvig Aberg.
MacIntyre, who had missed the cut in his two previous appearances in this event, arrived on the 18th tee in the company of Meronk and Yannik Paul, his closest challenger on the European Points list, needing a par to make it through on this occasion.
The Oban man found one of two fairway bunkers from the tee before going through the back of the green with his approach, but, after holding his nerve to hole a testing three-and-a-half footer, the relief on his face was there to see.
“I am happy with the way I fought,” he said after signing for a 69 for a three-under total. “I missed so many putts. I was trying not to count them on the way round, but I just felt that every green I hit I was missing a putt from inside ten feet.
"I was fighting to stay inside the cut coming up the last and, thankfully, managed to just sneak over the line. The last two Thursday and Friday draws (he was paired with European captain Luke Donald in Prague last week) have been difficult on the mind with everything that’s going on - it’s been tough.”
Fitzpatrick, who needs a tie for seventh with one other player or better to jump above Tommy Fleetwood on the World Points list, followed an opening 63 with a 65 to lead by a shot from Swede Alexander Bjork (64), with Alex Fitzpatrick, Matt’s younger brother, one further back. Connor Syme (67) is the leading Scot on eight-under.