- Zlatko Junuzovic scores the only goal for the hosts
- Austria can qualify if they avoid defeat against Sweden on Tuesday
- Winless Moldova stay bottom of Group G
- Nicolae Milinceanu misses early chance for visitors
- Next games: Sweden v Austria, Moldova v Montenegro (8 September)
Zlatko Junuzovic scored the winner as Austria went seven points clear at the top of Group G, a narrow victory against Moldova edging them one step closer to qualification for UEFA EURO 2016.
Marcel Koller's men will travel to second-placed Sweden on Tuesday knowing that a point or more will be enough to finish the job, having dropped just two points in seven matches.
Delivering an assured, if slightly nervous display, at the Ernst-Happel-Stadion in Vienna, the hosts eventually secured a win that leaves them on the verge of qualifying for the first time; their only previous finals appearance came as co-hosts in 2008.
Zlatko Junuzovic is mobbed after scoring Austria's winner
Home goalkeeper Robert Almer was called into action on the half-hour as Artur Patraş's corner crept through a host of defenders to land conveniently at the feet of Nicolae Milinceanu. The Petrolul Ploiești striker, however, did not have enough time to apply any degree of accuracy to his effort and Austria escaped.
After the break Marko Arnautovic combined neatly with Julian Baumgartlinger before finding David Alaba in space on the edge of Moldova's area, only to watch his team-mate fire well wide.
Alaba, the Bayern München midfielder, was not disheartened and combined well with Marc Janko moments later, unleashing a fierce drive which keeper Ilie Cebanu fumbled. Junuzovic seized upon the loose ball and slotted in to send the crowd home happy.