The Potters have not won a game since seeing off Coventry in the previous round, with three losses and three defeats, but started well against a Cottagers side showing 10 changes from their midweek defeat by Manchester City.

South Korean midfielder Bae Jun-ho capped a fine move by putting Mark Robins’ team ahead after 19 minutes but they were overpowered as their Premier League opponents settled after the interval.

Brazilian winger Kevin got his reward for a livewire performance in the 55th minute, sending a first-time effort into the bottom corner after cutting in from the left, and a self-inflicted error cost the hosts dear with six minutes remaining.

Under siege for long periods, goalkeeper Tommy Simkin attempted a short pass to Tatsuki Seko, who was caught daydreaming by Fulham’s captain-for-the-day Reed. He collected the ball as Seko tumbled to the turf, finished calmly and sealed the London club’s place in the next stage.

Both sides had early sights of goal, Stoke’s Ashley Phillips missing at the back post after meeting a floated free-kick and Reed shooting over from the edge of the box after Rodrigo Muniz did well to keep the attack alive.

For Fulham, American full-back Antonee Robinson was a lively starter down the left but the raft of changes made for some careless passing that threatened to invite trouble. The home side drew the first save, cup regular Benjamin Lecomte blocking with his feet after Sorba Thomas rifled a low shot through a crowd of bodies.

The opener duly arrived and it was expertly worked, Tomas Rigo feeding Eric Bocat, who spotted Jun-ho’s run and found him with the cross. After one touch to tee himself up, the number 10 smashed the ball past Lecomte at pace for a deserved lead.

Fulham were stung into action and twice came close courtesy of Kevin, whose curling effort would have nestled in the top corner had Simkin not had the dive to match. When he turned creator, standing up a cross for Alex Iwobi to run on to, the experienced midfielder headed wide by a yard with time and space to do better.

The lead held until half-time despite Kevin’s growing influence, which saw him clear the crossbar after Oscar Bobb’s lay-off and draw a strong, low save from Timkin in added time.

Stoke were on the back foot after half-time but turned defence into attack when Rigo’s brave intervention set Lamine Cisse running. He raced into space and sent a curling strike that glanced the post after a fingertip save from Lecomte.

With danger averted, Fulham levelled with their next move. It was no surprise to see Kevin’s name up in lights, feeding a low ball in from the flank then lashing into the bottom corner as it deflected back to him.

Fulham were a different team for the next 20 minutes, pouring forward in waves as Stoke battled to clear their lines with Kevin, Bobb and Iwobi swarming the box.

After a long series of clearances, the resistance buckled with a costly lapse in concentration. Seko failed to respond to Simkin’s short pass and Reed snuck in to steal possession and settle the tie with a clean low strike.