Everton trounced Championship side Preston North End 4-0, with Thierno Barry scoring his first hat-trick for the Toffees at Deepdale, while Tottenham Hotspur beat second-tier visitors Charlton Athletic 5-1 in North London.
Newcastle, the 2025 winners, went behind in the 19th minute at home on Wednesday against their Championship opponents when Isaac Price fired in a curling free kick and diving goalkeeper Ewen Jaouen was unable to keep it out.
The Magpies, who reached at least the semi-finals in three of the past four seasons under now-departed manager Eddie Howe, equalised in the 38th from close range through new signing Bazoumana Toure.
Substitute Barnes then lashed the ball into the net from close range minutes after coming on to put Newcastle ahead in the 48th, but Lewis Hall conceded a penalty in the 76th with a handball and Price equalised from the spot.
Hall hit the post moments later as he tried to make amends before Barnes grabbed his second goal of the night to calm nerves in the 81st.
Spanish midfielder Nico Gonzalez was presented to the crowd before the game after completing his STG52 million ($A99m) move from Manchester City to St James' Park.
Everton boss David Moyes had a comfortable return to the club where he started his managerial career, with Barry scoring in the 25th, 59th and 70th before Brennan Johnson added a fourth.
Tottenham, thrashed 3-0 at Brentford in their Premier League opener, were 2-0 up by half-time with goals from Mikey Moore (41st) and Dominic Solanke (45th).
Kevin Danso scored the third in the 67th and new signing Savinho opened his account on his debut in the 82nd. Ben Davies provided the cherry on the cake with a fifth in the 85th, assisted by Savinho, before Lloyd Jones pulled one back for Charlton.
Spurs' reward is now a trip to Anfield to meet Liverpool, where Andy Robertson will make a quick return to Merseyside after his off-season move to London.
League One Bradford City beat Championship side Burnley 4-2 on penalties after a goalless 90 minutes.
Nottingham Forest, beaten 2-0 by Leeds United in an all-Premier League match on Tuesday, are the only top-flight side to go out at the first hurdle so far.
The second round is the starting point for the 11 Premier League clubs not involved in European competition, with the other nine joining in the third round.
Draw: Second round: Chelsea vs Luton Town, Fulham vs AFC Wimbledon.
Third round: Liverpool vs Tottenham, Manchester United vs Brighton, Sunderland vs Hull, Ipswich vs Arsenal, Coventry vs Aston Villa, Chelsea/Luton vs Leeds, Manchester City vs Norwich, Bournemouth vs Lincoln, Crystal Palace vs Middlesbrough, Millwall vs Newcastle, Everton vs Wolves, West Ham vs Fulham/Wimbledon, Reading vs Brentford, Fleetwood vs Sheffield United, Leyton Orient vs Bradford, Peterborough vs Barnsley.
