West Ham booked a fifth-round FA Cup tie at boss David Moyes' former club Manchester United with a comfortable 2-0 win at Derby.
Jarrod Bowen's third goal in two games gave the Hammers a first-half lead and Michail Antonio headed home their second five minutes after break.
The Londoners made it back-to-back wins after beating Everton 2-0 to climb out of the Premier League's bottom three nine days go and rarely needed to hit top gear as they halted League One side Derby's 19-game unbeaten run.
Paul Warne's side are flying high in fourth place in the third tier and there were high hopes of an upset among the home faithful before kick-off in a Pride Park crowd of 25,308.
Derby forward Tom Barkhuizen wasted no time in breaching West Ham's defence, scampering clear in the opening minute before his cut-back was scrambled clear.
Bowen shot tamely at Derby goalkeeper Joe Wildsmith soon after, but was not so wasteful in the 10th minute.
Antonio's ball over the top caught Derby flat-footed and Bowen volleyed home Tomas Soucek's neat headed pass from six yards.
Derby's best move of the half saw James Collins volley just off target after Barkhuizen had run on to Craig Forsyth's dinked pass to pick out the Derby striker with a fine cross.
Barkhuizen and Nathaniel Mendez-Laing offered Derby's best hopes of getting back on level terms before the break, but they had no shots on target in the first period.
The good news for Rams fans at the break was their side were still in the tie against a top-flight side who were not at their best.
But five minutes into the second period the home side fell 2-0 behind. Derby skipper Curtis Davies's sliced clearance span into Bowen's path down the right and his cross was headed in at the far post by Antonio after deflecting off Forsyth.
Warne sent on four substitutes - Eiran Cashin, Liam Thompson, Lewis Dobbin and Tony Springett - soon after and their fresh legs gave Derby a lift.
Haydon Roberts was an inch away from connecting fully with Dobbin's excellent cross, but the Rams were soon back-pedalling again.
Bowen was denied in quick succession by Wildsmith's point-blank save and Cashin's last-ditch tackle and Ben Johnson's angled drive was kept out by the Derby goalkeeper.
The Rams were full of endeavour until the final whistle and Dobbin was close to being rewarded for an impressive cameo display when shooting straight at Alphonse Areola, but on the night County could not bridge the gulf in class.