Spurs have jumped above Liverpool and are now just a point behind West Ham United, who earlier blew a 3-0 lead to draw 3-3 with Arsenal.
Arsenal are now ninth, a point above Villa.
Meanwhile, Leicester City are through the semi-finals of the FA Cup for the first time since 1982 after beating Manchester United 3-1.
Leicester will face Southampton for a place in the final at Wembley.
Chelsea have drawn Premier League leaders Manchester City in the other semi-final after the Blues beat Sheffield United 2-0.