Steven Gerrard's side had striker Alfredo Morelos sent off early on but they took the lead through James Tavernier’s penalty on the half-hour mark and were on course for victory until the substitute struck right at the end.
In the day's later game, Hibernian saw off Motherwell 3-0 at Easter Road thanks to goals from Stevie Mallan, Oli Shaw and Martin Boyle.
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