Martin O'Neill's side require wins for Croatia and Cyprus tonight, while they also need Italy to prevent Norway from winning and for a draw between Turkey and Iceland.
After the wins last night for Sweden, Slovakia and Slovenia, Ireland now look likely to be among the second seeds for the play-off draw, which takes place on Sunday.
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Wales are also among the teams in action tonight – despite having already qualified for next summer's Championships, Chris Coleman's side have a chance to top Group B if they win at home to Andorra and table-toppers Belgium slip-up at home to Israel.
Kick-off in all of tonight's qualifiers is at 7:45.
