The pair had gone into the rally level on points, but Loeb will take a 30.6-second lead over Hirvonen's teammate Jari-Matti Latvala into Saturday's second leg, with Hirvonen a further 24.2 seconds adrift.
Latvala had led going into the sixth and final stage of Friday's first leg, but he hit problems, losing 46.2 seconds to see his advantage disappear.
Hirvonen, who was slowed by dust from cars running in front of him in the opening stages, had built up speed as the day had gone on, but he looks unlikely to be able to catch Loeb in the remaining two days of the event.
A victory for Loeb would mean that a win for Hirvonen in the final round of the championship in Britain next month would not be enough to take the title unless Loeb finished no higher than third.
It had been a three-way fight for the title going into the event, but Sebastien Ogier, Loeb's Citroen teammate, who had only been three points adrift of the lead pair, lost more than 90 seconds due to a puncture on stage five and his hopes of a podium finish are slim.
He is 1min 53secs behind his teammate, and his main focus will now be on helping Loeb by trying to catch Hirvonen and limiting the number of points that the Finn takes from the event.
Sheikh Khalid Al Qassimi, driving the third Abu Dhabi car, is in 16th place, more than four minutes off the pace.
Saturday's itinerary sees the drivers tackle six stages, with six more Sunday on the final day.