At Stevenage, Johnny Heitinga and Magaye Gueye were the other scorers for Everton, whose manager Roberto Martinez won the FA Cup with Wigan last season. The result was overshadowed, though, by the horrific-looking injury to Oviedo in the 14th minute.
Oviedo was taken to hospital and Everton tweeted that he has a suspected broken leg.
Non-league Kidderminster’s run to the last 32 has been the feelgood story of this season’s competition, but it came to an end at Sunderland, who were playing three days after beating Manchester United on penalties to reach the League Cup final against City.
Charis Mavrias scored the only goal in the fifth minute.
In other results, Southampton beat Yeovil 2-0; Swansea won 2-1 at Birmingham; Hull defeated Southend 2-0; Cardiff were 1-0 winners at Bolton; Huddersfield lost at Charlton 0-1; Port Vale went down at Brighton 1-3 and Rochdale were defeated at Sheffield Wednesday 1-2.