Nigeria international, Brown Ideye, scored twice as resurgent West Brom put four goals past West Ham to reach the FA Cup quarter-finals for the first time since 2008.
Brown Ideye side-footed West Brom ahead after 20 minutes before a 25-yard shot from James Morrison made it 2-0.
Ideye headed the third goal from eight yards early in the second half.
West Brom are still fighting against relegation in the Premier League but manager Tony Pulis – who has lost just one in his first eight games in charge – had made it clear he also wants a sustained cup run.
The performance of his side reflected that as they moved to within two wins of giving Pulis the chance to make amends for the defeat he suffered as Stoke manager against Manchester City in the 2011 FA Cup final.
West Brom dominated throughout against a West Ham side who, according to manager Sam Allardyce, were also intent on trying to win the trophy with no fears of their own about league safety.
Ideye, who initially struggled following his arrival from Dynamo Kiev for a reported £10m last summer, has now scored four goals in his last three games to take his tally for the season to five.
The Nigeria international tapped home the opening goal from a Craig Dawson cross and West Brom almost doubled their lead when Craig Gardner, playing in place of the cup-tied Darren Fletcher, struck the bar from 35 yards.
West Ham’s reprieve was short-lived as Morrison robbed Mark Noble before firing home and when Ideye headed in a cross from Stephane Sessesgnon 12 minutes into the second half a comeback never looked likely.
Amalfitano was dismissed 10 minutes after coming on for first kicking out at Brunt and then raising his hand to the Albion midfielder’s face in the minor skirmish that followed. Referee Martin Atkinson, who had issued a yellow card for the initial offence, then reached into his back pocket and pulled out the red.
Minutes later West Ham’s misery was complete when Berahino found himself in space on the right of the penalty area and he drilled home his 16th goal of the season from an acute angle, beating keeper Adrian at his near post.