Millwall reached the FA Cup quarter-finals thanks to a 1-0 victory over League Two AFC Wimbledon on Saturday.
The Championship side saw off their London neighbours at Kingsmeadow courtesy of a fifth-minute header from Murray Wallace.
Wimbledon stunned West Ham with a 4-2 victory in round four, but another shock appeared unlikely once Wallace turned the ball in from six yards out after a fine run and cross from Ryan Leonard.
The attacking flair that caused the Hammers so many problems seemed to desert the home side, who failed to register a shot on target until Michael Folivi's 61st-minute effort was saved by Jordan Archer.
Aaron Ramsdale kept the advantage limited to one goal with a good save from Leonard, while Lee Gregory headed wide from a promising position.
But Millwall survived any threat of a late comeback to reach the last eight for the second time in three seasons, joining Watford and Brighton and Hove Albion.