Nani continued to torment the Albion defence and whipped in another great ball minutes later that just evaded Javier Hernandez, who decided not to gamble.
However, a great chance fell to the visitors as Berahino headed wide after an inviting ball was put into the box.
Rooney then got in behind the Albion defence to meet a cross with a header, but the United striker could only direct his effort over the bar.
The best chance of the half came late on as Anderson produced an athletic diving header that came back off the bar, before Shinji Kagawa showed good feet to beat two defenders but failed to apply the finish.
United were dealt a massive shock after the break when Amalfitano produced a world-class run to get past a lacklustre United defence, before lifting the ball over David de Gea to give Albion a 1-0 lead.
Rooney ensured that the visitors' lead didn't last too long as he levelled proceedings in the 57th minute with a bizarre, unintentional goal.
Poor United marking almost led to their downfall again as Albion swung in a corner, only for Jonas Olsson's header to crash onto the post.
Having not taken enough warning from Albion's attacking play, United were made to pay after a great move from the visitors allowed Berahino to finish well and give them a 2-1 away lead.