Leeds, currently top of League One (division three) but Liverpool's equals in the top division for decades until their relegation five years ago, succumbed to a 66th minute goal scored by 20-year-old French striker David Ngog.
Championship (second division) side Barnsley did manage a win over Premier League opposition when they beat last season's semi-finalists Burnley 3-2 at Oakwell with Argentine defender Hugo Colace scoring the 75th minute decider.
Portsmouth, bottom of the Premier League after losing their opening league six games of the season, won 3-1 at League One (third division) Carlisle United, but had to come from behind before advancing.
Premier League sides Arsenal, Blackburn Rovers, Sunderland and Stoke City all went through to Saturday's fourth round draw.
Arsenal, fielding eight teenagers, beat Championship leaders West Bromwich Albion 2-0 at home with 18-year-old London-born striker Sanchez Watt opening the scoring on his debut and Carlos Vela adding the other.
Sunderland were 2-0 winners over Premier League rivals Birmingham City while Blackburn Rovers won 1-0 at Championship side Nottingham Forest.
In a seven-goal thriller at the Britannia Stadium Stoke City beat Championship side Blackpool 4-3 with Andy Griffin scoring the winner six minutes into stoppage time after Blackpool had lead 2-0 early in the second half.
(Editing by Justin Palmer)