Leeds and Southampton were the Premier League casualties in the second round of the League Cup on Wednesday as League One Hull won a Yorkshire derby 9-8 on penalties at Elland Road, while Saints lost 2-0 at home to Brentford.
On their first appearance in the top-flight for 16 years, Leeds were unlucky not to hold Liverpool to a thrilling draw at Anfield on Saturday, but Marcelo Bielsa's decision to make 11 changes backfired as his side were far less clinical against a team two divisions below them.
Mallik Wilks's early deflected effort gave the Tigers something to hold on to and, despite handing club Spanish international forward Rodrigo his first start, Leeds failed to muster a response until deep into stoppage time when Ezgjan Alioski fired home.
A marathon shootout followed with both sides missing just one of their first eight penalties before Jamie Shackleton's spot-kick was saved and Alfie Jones sent Hull into round three.
Southampton boss Ralph Hassenhuttl named a strong side at St Mary's but still got no response from their disappointing start to the season at Crystal Palace on Saturday.
Brentford narrowly missed promotion to the Premier League for the first time when they lost the playoff final to Fulham last month, but showed they do have the quality to compete with top-flight teams despite losing top scorer Ollie Watkins to Aston Villa.
Two goals in six minutes towards the end of the first half from Christian Norgaard and Josh Dasilva handed the Bees a place in the third round.
Everton enjoyed a far more comfortable night as Carlo Ancelotti's much-changed team were still too good for League Two Salford City, who are part-owned by a cast of former Manchester United stars including David Beckham.
Michael Keane was the only man to keep his place in the Everton side form Sunday's impressive 1-0 win at Tottenham and opened the scoring on eight minutes.
Gylfi Sigurdsson then put the tie to bed with his 100th goal in English football before Moise Kean added a late penalty.
Fulham and West Brom bounced back from being soundly beaten in their first matches back in the top-flight last weekend.
Aleksandr Mitrovic was recalled to the Scott Parker's starting line-up and his header earned Fulham a 1-0 win at Ipswich.
West Brom eased past League Two Harrogate 3-0 thanks to goals from Rekeem Harper, Hal Robson-Kanu and Callum Robinson.
Bristol City were also comprehensive 4-0 winners over Northampton.