Southampton and Leeds became the first Premier League casualties of the Carabao Cup after they were beaten by Brentford and Hull City respectively.
The second round continued on Wednesday evening with five top-flight sides in action, while there was also disappointment for League One side Northampton Town and fourth tier outfit Salford City.
However, the biggest shock of the night was inflicted on Marcelo Bielsa's Leeds, who off the back of an encouraging display at Anfield, succumbed to a penalty defeat at home to third tier side Hull City. The Tigers were good value for their 1-0 lead, but were pegged back in stoppage time by Ezgjan Alioski's late equaliser. It counted for nothing in the end, as the visitors ran out 9-8 winners in a penalty shootout.
Ralph Hasenhuttl also saw his side start the 2020/21 campaign off with back-to-back defeats. Southampton welcomed the Championship's Brentford to St. Mary's, but were undone by a first half late show from the Bees. Goals from Christian Nørgaard and Josh Dasilva on the stroke of half time securing a 2-0 win.
Everton also booked their place into the third round with a 3-0 win over Salford City in a game the home side dominated. Michael Keane, Gylfi Sigurðsson and a Moise Kean penalty did the damage as Carlo Ancelotti's side cruised against the League Two outfit.
It was a similar story for West Brom as they brushed aside Football League newcomers Harrogate Town 3-0 at the Hawthorns. Goals from Rakeem Harper and Hal Robson-Kanu in the first half were added to by Callum Robinson after the restart, ending the Sulphurites journey in the competition.
Elsewhere, Fulham secured a narrow victory over League One Ipswich at Portman Road - Aleksandar Mitrović's goal handed the visitors a deserved 1-0 win. On the other side of England, Bristol City had no problems taking on Northampton at Ashton Gate, with strikes from Chris Martin, a double from Kasey Palmer and a solitary Antoine Semenyo strike earning them a comfortable 4-0 win.