The Blues had taken the lead, but the match turned early in the second half when defender Trevoh Chalobah was sent off.
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The Seagulls then seized control, with Danny Welbeck netting twice to help his team secure a valueable win.
“We suffered in the first minutes and conceded the goal but then we started to play. We created chances and were better out of possession and were much better overall,” said Hurzeler.
“Sometimes when you are a man up it can be more difficult as the other team are trying to defend. But we stayed patient, we stayed calm and we opened the gaps by playing from left to right.
“And then when you have individuals with the quality that we have it can make a difference.”