Chelsea and Everton barely advanced to the third round of the League Cup against fourth-tier competition on Wednesday.
Chelsea fell behind against AFC Wimbledon at Stamford Bridge but came back to win 2-1 thanks to Enzo Fernandez's first-ever goal for the team.
Struggling Everton overcame a late deficit to defeat Doncaster 2-1.
Sheffield United were not as fortunate as their Premier League counterparts, the Blades crashing out against third tier Lincoln on penalties.
Mauricio Pochettino made seven changes to the side that beat Luton 3-0 for his first win as Chelsea boss on Friday.
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Ian Maatsen, Lesley Ugochukwu and Mason Burstow made their first starts, while Diego Moreira was handed his debut.
Still looking for his first trophy in English football after spells with Southampton and Tottenham, Pochettino might have feared his first attempt with Chelsea was going to end in abject failure when Wimbledon struck in the 19th minute.
Chelsea keeper Robert Sanchez collided with Harry Pell as he came off his line in a failed attempt to collect a cross, conceding a penalty that James Tilley calmly stroked home.
After being fouled by Alex Pearce, Chelsea's Noni Madueke converted from the penalty spot to tie the score just before halftime.
After coming off the bench, Fernandez gave Chelsea's midfield greater poise, and the Argentine World Cup winner gave his team the lead in the 72nd minute.
After moving from Benfica for £106 million in January, Fernandez eventually scored, taking advantage of an error in the Wimbledon defense.
Everton boss Sean Dyche made just four changes in a bid to avoid a giant-killing at the Eco-Power Stadium.
But Everton laboured throughout a dismal first half performance and fell behind in the 44th minute.
Joe Ironside punished sloppy defending to head Tommy Rowe’s cross past Jordan Pickford despite the visitors’ appeals for offside.
Dyche sent on Portuguese striker Beto, signed from Udinese for £30 million this week, for his debut at the start of the second half.
Beto scored 21 Serie A goals in two seasons with Udinese and the 25-year-old quickly put his predatory instincts on display in a Toffees shirt.
Sprinting onto Abdoulaye Doucoure’s hopeful pass forward in the 73rd minute, Beto got behind the Doncaster defence and guided a clinical finish into the far corner for Everton’s first goal this season.
Arnaut Danjuma then spared their blushes with a composed strike from the edge of the area in the 88th minute.
Sheffield United’s miserable start to the season hit a new low with a 3-2 penalty shoot-out loss to third tier Lincoln at Bramall Lane.
The Blades suffered their fourth straight loss as a dull 90 minutes ended scoreless thanks to Lincoln goalkeeper Lukas Jensen's saves on Louis Marsh and Benie Traore's penalty shots.
