Ultimately, it was another Premier League team, Sheffield United, that were on the end of an unlikely upset, losing a penalty shootout to third-tier Lincoln City for the biggest shock of the second round on Wednesday night.
Noni Madueke equalised with a penalty of his own in first-half added 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.
"It was tough," Blues boss Mauricio Pochettino said.
"That's the beauty of the competition for any club, (when you're) a Premier League club it's always difficult to play a team like this, that belongs to this level in League Two. Always the motivation and the desire.
"Many positive things. Of course, we have a squad and players that were rested and were on the bench in case we needed. They were fresh to go into the game and of course to help the team achieve what we wanted."
Everton left it much later for their 2-1 win at Doncaster Rovers, with Beto — a Portuguese striker who only joined from Italian Serie A club Udinese one day earlier — and Arnaut Danjuma scoring in the 73rd and 88th minutes, respectively, to complete a nervy comeback.
Everton have 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.
"I am really happy to score on my debut to help the team win the game," Beto told Sky Sports.
"I can't promise goals but I promise effort and to work hard. I will try to help the team to score goals."
Like Everton, Sheffield United have 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, United lost the shootout 3-2.
Elsewhere, Burnley scored in the 90th minute 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 Rovers crushed fourth-tier Harrogate Town 8-0.
That was Blackburn's biggest away win in their 148-year history.
Ipswich Town v Wolverhampton Wanderers
Exeter City v Luton Town
Aston Villa v Everton
Port Vale v Sutton United
Bradford City v Middlesbrough
Bournemouth v Stoke City
Lincoln City v West Ham United
Chelsea v Brighton & Hove Albion
Salford City v Burnley
Fulham v Norwich City
Blackburn Rovers v Cardiff City
Liverpool v Leicester City
Mansfield Town v Peterborough United.