Tammy Abraham's strike was just his third goal for Aston Villa since he rejoined the club from Besiktas in January.
His last goal – a late equaliser against Leeds seven league games ago in February – was equally dramatic.
Villa need just six more points to ensure Champions League qualification, with Premier League games against Fulham, Tottenham, Burnley, Liverpool and Manchester City still to come.
Abraham may have got the winner but the striker he replaced, Ollie Watkins, was Villa's star with two goals and an assist.
The 30-year-old's performance will also have helped his chances of making England's World Cup squad.
Watkins has now scored 16 goals in all competitions this season and five in four games since he was left out of Thomas Tuchel's last England squad in March.
Harry Kane is the only Englishman playing in the top five leagues to have scored more goals.
