The Japan international settled a trying contest on the stroke of half-time to give the 05ers a slender but potentially decisive advantage ahead of next week's trip to Greece.
Okazaki on cue
Well-drilled and chasing a sought-after away goal, the Greek outfit made life hard for the 2013/14 Bundesliga season's seventh-placed side. Ziguy Badibanga was a constant thorn in the side of Mainz left-back Jo-Hoo Park, although it was Pablo Mazza who went closest to breaking the deadlock when his free-kick rattled the crossbar with Loris Karius beaten.
Mainz took heed of the warning and got the breakthrough late in the half, albeit against the run of play. Park nodded a Christoph Moritz cross into the path of Okazaki, who banished memories of his country's disappointing FIFA World Cup campaign in Brazil with a cool finish from close range. Pablo de Blasis should have levelled as the visitors turned the screw, but Mainz dug their heels in to give Hjulmand a debut win as head coach.
Mainz: Karius - Jara, Noveski, Bell, Park (Diaz 71') - Geis, Baumgartlinger (Brosinski 60') - Moritz, Malli, Koo (Zimling 77') - Okazaki
Asteras: Theodoropoulos - Lluy, Goian, Zisopoulos, Panteliadis - Mounafo (Tsokanis 72'), Kourbelis - Badibanga (Kitoko 81'), Rolle (Sankare 65'), Mazza - de Blasis
Goals: 1-0 Okazaki 45'