Leeds, which was the talk of the Premier League after its thrilling 4-3 defeat to champion Liverpool at Anfield last weekend, only pushed the match against rival Hull City to a penalty shootout thanks to a 93rd-minute equaliser from Ezgjan Alioski.
But the Tigers prevailed 9-8 in the shootout, Alioski missing Leeds's second spot-kick before Jamie Shackleton failed later on to hand Hull the tie.
Southampton, beaten in the Premier League at the weekend by Crystal Palace, lost 2-0 to Brentford in their clash, the Bees scoring two quick-fire goals in the first half to seal the match.
Christian Norgaard broke the deadlock from a corner, before Josh Dasilva put the finishing touch on a well-crafted move five minutes later, with Saints unable to find a reply, leading to an honest assessment from coach Ralph Hasenhuttl.
🗣 "There are too many things missing from our game."— Southampton FC (@SouthamptonFC) September 16, 2020
An honest review from the manager following tonight's defeat:
Brentford's reward is a third-round tie with West Brom, which put on a show for the still empty stands at The Hawthorns to breeze past Harrogate Town, newly promoted to League Two after winning last season's National League play-off final.
🗣 "A good win, a good performance, and more good minutes into the players"— Brentford FC (@BrentfordFC) September 16, 2020
Thomas couldn't have asked for much more as we booked our spot in Round Three of the @Carabao_Cup #BrentfordFC #SOUBRE pic.twitter.com/wUkeDolcK4
But the Sulphurites were no match for Slaven Bilic's side, which fired home some sensational goals through Rekeen Harper and Hal Robson-Kanu in the first half before Callum Robinson finished a tidy move in the 77th minute to wrap it up.
Elsewhere, Fulham bounced back from being soundly beaten in its first match back in the top-flight with a 1-0 win at Ipswich Town, Aleksandr Mitrovic scoring the goal on his return to Scott Parker's starting line-up. The Cottagers will play Sheffield Wednesday in the third round.
Bristol City was another comprehensive winner in the round, thrashing Northampton Town 4-0 in their match, while Everton also did it reasonably easy against Salford City, winning 3-0.