Goals from Manuel Lanzini and Jarrod Bowen ensured the Hammers' safe passage into the fourth round of the competition, where they will travel to Kidderminster Harriers at the start of February.
It was a spirited but, ultimately, toothless display from Leeds, who are still trying to survive in the Premier League with injuries to key men wreaking havoc to their season.
As well as losing Patrick Bamford, Leeds are without talisman and England Euro 2020 star Kalvin Phillips until March after the 26-year-old underwent hamstring surgery in December.
Phillips was instrumental in the Three Lions' midfield alongside Rice during a glorious summer when Gareth Southgate's side fell agonisingly short against Italy in the final.
Despite the dynamic duo working well together, Leeds fans were quick to remind Rice who they felt the superior member of that famous midfield was during a break in play on Sunday - with Rice taking the jokes rather well.
Twitter user Jonny Good wrote, 'Great lad and great player', whilst Darren Turner said, 'Got a lot of time for Declan Rice. Good player with his feet firmly on the ground. Hope he and Kalvin can boss the England midfield for years to come.'
Like Phillips, Rice has been linked with a move away following his heroics at the European Championship, yet Jim White confirmed on talkSPORT the 22-year-old would not be going anywhere in January.
"I've got some interesting news on Declan Rice," he said. "West Ham fans; don't panic.
"He ain't going anywhere, not in this window. That is for sure."