Qualification had looked dead and buried before the header.
Liverpool are just one point off the Champions League places after a dramatic 2-1 win away to West Brom in the Premier League.
Goalkeeper Alisson scored deep into injury time to claim all three points for Jurgen Klopp's side.
Liverpool are one point behind fourth placed Chelsea with two games to play
The Brazilian keeper dedicated the goal to his late father, who drowned near his home in February:
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Athlone Town Knocked Out Of All-Island Cup
Limerick See Off Offaly In Senior Camogie Championship
Athlone Town Suffer Defeat Away To UCD In First Division