Chelsea and Everton narrowly avoided humiliating League Cup exits against fourth tier opposition as they scraped into the third round on Wednesday.
At Stamford Bridge, Chelsea trailed against minnows AFC Wimbledon before recovering to win 2-1 thanks to Enzo Fernandez's first goal for the club.
Struggling Everton came from behind in the closing stages to beat 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.
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.
Chelsea equalised on the stroke of half-time when Noni Madueke netted from the spot after the winger was fouled by Alex Pearce.
Fernandez added more composure to Chelsea's midfield after coming off the bench and the Argentine World Cup winner put his side ahead in the 72nd minute.
Taking advantage of a mix-up in the Wimbledon defence, Fernandez slotted home to finally get on the scoresheet after arriving from Benfica for £106 million in January.
Beto revives Everton
After three successive defeats to start the league season, Everton were pushed to the brink of more misery by a Doncaster side sitting bottom of fourth tier League Two.
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.
After a drab 90 minutes ended goalless, Lincoln goalkeeper Lukas Jensen saved spot-kicks from Louis Marsh and Benie Traore to hand the Blades a fourth successive defeat.
Burnley won 1-0 at fellow top-flight side Nottingham Forest thanks to Zeki Amdouni's close-range volley in second half stoppage-time.
In the night's other tie, Championship side Blackburn thrashed fourth tier Harrogate 8-0.
