Striker Rooney, who also scored two headers when his side beat AC Milan in the Champions League last week, took his tally for the season to 27 - with 19 of those goals coming in his last 19 matches.
Substitute Michael Owen added the third in the 80th minute, two minutes after replacing goal machine Rooney who executed both headers with real power from crosses by Antonio Valencia after 38 and 55 minutes.
The only blemish for United was revealed when manager Alex Ferguson said afterwards that defender Rio Ferdinand, who missed the game with a twinge in his back, was also out of Sunday's League Cup final against Aston Villa at Wembley.
The centre back is also now a doubt for England's friendly against Egypt at the same stadium three days later.
"He felt a twinge in his back this morning... and we couldn't risk it," Ferguson told Sky Sports. "He won't be playing on Sunday."
Ferguson, though, was pleased with United's win which ended 13th-placed West Ham's recent revival. Gianfranco Zola's men had lost once in six matches but were always second best on Tuesday.
"It was a good attitude from the players, they were hungry for the victory and did very well. West Ham have been doing very well recently so it was a good result for us," Ferguson added.
He reshuffled his side after Saturday's 3-1 league defeat at Everton, making five changes including bringing back defender Nemanja Vidic and goalkeeper Ben Foster.
