Liverpool teenager Curtis Jones scored twice in a 7-2 victory over Lincoln in the League Cup, and defending champion Manchester City edged past Bournemouth 2-1.
Liverpool advanced to a fourth-round meeting next Thursday with Arsenal, which also plays at Anfield in the Premier League on Monday.
Phil Foden’s late goal secured City’s progress to a match next week with Burnley.
The 19-year-old Jones scored Liverpool’s third and fourth goals before halftime, cutting in from the left on both occasions to curl in right-footed shots, and was the visitors’ main creative force in midfield.
Jones also won the free kick from which Xherdan Shaqiri whipped in the opener for his first goal in over nine months.
Takumi Minamino continued his promising start to the season with a first-time shot in the 18th minute.
All of Liverpool’s four first-half goals were scored from at least 20 yards.
Eighteen seconds after the break Minamino added another, stabbing in Harvey Elliott’s smothered effort.
Marko Grujic scored his first for the club almost five years after joining, and Divock Origi wrapped up the rout in the 89th with his ninth goal in 12 League Cup matches. Tayo Edun and Lewis Montsma had made it 5-1 and 6-2 by scoring for third-tier side Lincoln.
Spurs awarded bye
Tottenham have been awarded a bye into the fourth round of the League Cup after their tie with Leyton Orient was called off on Tuesday following a spate of coronavirus cases at the League Two club.
Fourth-tier Orient tried to rearrange the game but League Cup rules mean that they must forfeit the tie, allowing Spurs to go through to play Chelsea.
Spurs will now prepare for four games in eight days, starting with the visit of Newcastle on Sunday.
Jose Mourinho’s men then host Chelsea on Tuesday, host Maccabi Haifa in Europa League qualifying on Thursday and travel to Manchester United a week on Sunday.