Man City, Leicester, Everton through to League Cup quarters
City earned a routine 3-1 victory against fellow Premier League team Southampton, which was still reeling from Friday's 9-0 home loss to Leicester.
Jack Stephens headed in a late consolation goal for Southampton.
Everton also beat Premier League opposition, with a 2-0 win over struggling Watford.
Mason Holgate scored his first goal for Everton in the 72nd and Richarlison sealed the match in stoppage time.
Leicester won 3-1 at Burton Albion to deny the League One side another potential run to the semifinals.
Strikes from Kelechi Iheanacho and Youri Tielemans gave Leicester a two-goal cushion at halftime. Liam Boyce pulled one back early in the second half but Leicester made sure of a place in the quarterfinals for the third successive year when substitute James Maddison struck in the final minute.
Burton beat Aston Villa, Burnley, Nottingham Forest and Middlesbrough en route to the last four of last season's competition.
Elsewhere, Oxford United beat fellow League One side Sunderland on penalties after the match had finished 1-1 and Colchester United won 3-1 at Crawley Town in a match between two League Two sides.