The Olympiakos striker scored either side of Dimitris Salpingidis' goal to seal a vital first-leg win, although Bogdan Stancu kept the visitors in with a chance of progressing
The Olympiakos star - who has been in superb form this season - scored either side of a Dimitris Salpingidis strike to cancel out Bogdan Stancu's early equaliser and ensure they go into next week's second leg in Bucharest as favourites to qualify.
Mitroglou claimed his first with a cushioned volley, before the visitors equalised five minutes later courtesy of Stancu's header.
Salpingidis regained the lead for Greece almost immediately with a tap in, and Mitroglou netted his second of the game in the 66th minute with another volley before Costin Lazar was sent off in stoppage time.
Both sides made three changes from their last group-stage qualifiers, with Borussia Dortmund's Sokratis Papastathopoulos among those to return for the hosts while Bogdan Lobont lined up in goal for Romania after first-choice goalkeeper Ciprian Tatarusanu injured his back in training.
The first action of note brought the opening goal in the 14th minute, as Salpingidis' lofted pass caught the visiting defence square and Mitroglou was left all alone to volley home from 12 yards.
Greece's lead lasted just five minutes, though, as Stancu nodded home from a tight angle at the far post after getting on the end of Gabriel Torje's free kick from the left.
That was the first goal Greece had conceded at home in their qualifying campaign, but it appeared to have no ill effect as they restored their advantage immediately.
Georgios Samaras found Vasilis Torosidis on the right hand side, and his cushioned first-time cross was converted by Salpingidis sliding in at the far post.
Six minutes before the break, Razvan Cocis wasted a golden chance to equalise when he blazed over from 10 yards following Cristian Tanase's penetrating pass.
After a quiet start to the second period, Mitroglou doubled the hosts' advantage midway through the half.
Samaras' left-wing free kick was flicked on by Konstantinos Katsouranis and the ball was allowed to travel across the box to Mitroglou, who volleyed home with aid of a deflection.
Lobont denied Mitroglou his hat-trick six minutes later, and substitute Theofanis Gekas had an 89th-minute strike ruled out for offside before Romania's substitute Lazar saw red in stoppage time for a second bookable offence.
Samaras then missed a golden opportunity to all but seal Greece's place at Brazil 2014 when he headed over from six yards in injury time, but Fernando Santos' side still head to Bucharest in control of the tie at the halfway stage.