The 25-year-old Mitroglou currently the top scorer in the Greek league at Olympiakos added his second in the 66th minute with another acrobatic effort to bury the ball provided by Georgios Samaras.
As his teammates shouted in celebration, Mitroglou urged caution.
"We had a great game and a great defense. We only conceded on a set piece. But we are only halfway through this and nothing is decided," he said.
"We are going to Bucharest as if the score is 0-0."
Romania ended the match with 10 men when substitute Costin Lazar was shown a second yellow card at the start of injury time.
Romania hosts Greece for the second playoff on Nov. 19.
Greece coach Fernado Santos said the win was well deserved.
"The players worked very hard and this paid off," the Portuguese coach said. "But we can't go into the next match acting like we have the advantage. That would be risky. We are going to fight very hard to stay ahead."
A despondent Victor Piturca, the Romania coach, described his country's chances of qualifying as being "very difficult indeed," and referred several times to his team's slow defense.
"I expected a difficult night and that's what it was," he said. "They took the lead so quickly after the equalizer. And I don't want to talk about the third goal. It looked like something that happens in a school playground."