Teams from the Football League Third and Fourth Division entered in this round plus Altrincham, Runcorn, Frickley Athletic and Telford United, were given byes.
Leeds United, managed by their former captain Billy Bremner, were pushing for promotion in the Second Division and making their first serious challenge for a major trophy in over 10 years.
After two minutes, Clive Allen scored his 49th goal of the season, heading past keeper Steve Ogrizovic at the near-post from a Chris Waddle cross.
Within seven minutes though, Coventry were level through Dave Bennett, a Cup Final loser in 1981 for Manchester City at the hands of Spurs.
Six minutes in, Mabbutt scored an own goal after Lloyd McGrath centred the ball and it took a deflection off of the Spurs defender's knee and over keeper Ray Clemence.