Ultimately, it was another Premier League team, Sheffield United, that was on the end of an unlikely upset, losing a penalty shootout to third-tier Lincoln for the biggest shock of the second round.
Noni Madueke equalized with a penalty of his own in first-half stoppage time and Fernandez, on as a 65th-minute substitute, grabbed the winner seven minutes later after a defensive mix-up to seal a 2-1 victory.
Everton left it much later for its 2-1 win at Doncaster, with Beto — a Portuguese striker who only joined the club from Udinese on Wednesday — and Arnaut Danjuma scoring in the 73rd and 88th minutes, respectively, to complete a nervy comeback.
Everton has started the Premier League with three straight losses, without scoring a goal, and the pressure would have piled on manager Sean Dyche if his team had been eliminated by an opponent sitting in last place in the fourth tier.
Like Everton, Sheffield United has no points from three games in the league but won't have League Cup games for respite in the coming weeks. After a 0-0 draw at home to Lincoln, Sheffield United lost the shootout 3-2.
Burnley scored in the 90th through substitute Zeki Amdouni, a recently signed Switzerland international, to win 1-0 at Nottingham Forest in an all-Premier League matchup and second-tier Blackburn crushed fourth-tier Harrogate 8-0.
That was Blackburn's biggest away win in its 148-year history.
The third round sees the teams involved in European competition this season enter the League Cup. The draw was made after Wednesday's games and there were five all-Premier League matchups picked out, with the standout being Newcastle hosting Manchester City. Manchester United begins its title defense at home to Crystal Palace.
Here's a look at the draw:
Ipswich vs. Wolverhampton
Exeter vs. Luton
Aston Villa vs. Everton
Manchester United vs. Crystal Palace
Port Vale vs. Sutton
Bradford vs. Middlesbrough
Bournemouth vs. Stoke
Lincoln vs. West Ham
Chelsea vs. Brighton
Salford vs. Burnley
Fulham vs. Norwich
Blackburn vs. Cardiff
Liverpool vs. Leicester
Newcastle vs. Manchester City
Mansfield vs. Peterborough
Steve Douglas is at https://twitter.com/sdouglas80
AP soccer: https://apnews.com/hub/soccer
Steve Douglas, The Associated Press