Fourth-tier AFC Wimbledon provided the shock of the night, beating newly-promoted visitors Ipswich 4-2 on spot kicks after playing out a lively 2-2 draw in south-west London.
Bournemouth were beaten 1-0 by West Ham United in an all-Premier League clash settled by an 88th-minute, deflected Jarrod Bowen goal at the London Stadium.
Newcastle had been playing for 19 seconds at the City Ground when Alexander Isak had a shot pushed away and Joe Willock, who soon limped off with a thigh injury, turned it in for his first goal since February.
With Italian midfielder Sandro Tonali returning from a 10-month ban for betting breaches and looking lively, Newcastle stayed ahead until Jota Silva equalised five minutes after the break.
"We are getting a player back who is a top-level player and it is about managing these first few games back," manager Eddie Howe had said of Tonali before the start.
Ipswich Town were 2-1 down and heading for the exit in regular time when Conor Chaplin headed in an 86th-minute equaliser to force the shootout.
The Dons' goalkeeper Owen Goodman then saved from Jack Taylor and Omari Hutchinson.
There were goals galore at Championship side Cardiff City who came from behind three times against Southampton only to lose 5-3 to the Premier League visitors after stoppage-time strikes by James Bree and Cameron Archer.
Premier League Wolverhampton Wanderers and Brentford, with England striker Ivan Toney absent pending interest from other clubs, beat Burnley and Colchester United 2-0 and 1-0 respectively.
Goncalo Guedes scored either side of half-time to send Wolves through while Brentford goalkeeper Hakon Valdimarsson saved a Jack Payne penalty after Keane Lewis-Potter scored in the 45th.
The second round marked the start of the competition for those Premier League clubs not playing in Europe this season, with clubs such as Manchester City, Chelsea and Arsenal joining in the third round.