The Parkhead side had lost the Scottish Communities League Cup final to Kilmarnock, the William Hill Scottish Cup semi-final to Hearts, and the Scottish Communities League Cup semi-final to St Mirren in their previous three appearances at the national stadium before they met United last month.
Brown said. "I agree with that (Hampden form had been sticky) in the last season and especially the semi-final against St Mirren but what the lads did against Dundee United (a 4-3 victory) here in the semi-final was incredible. It seemed to go end to end, we created a lot of chances, had a lot of possession and scored a lot of goals as well so it shows that we can win here if we really focus and put our heads towards it."
He added: "If we could win the cup it would be huge for us."
The Scotland midfielder knows all about the Leith club's own hoodoo. Hibs have not won the Scottish Cup since 1902 and Brown hopes to extend it by at least 12 more months in Sunday's final at Hampden Park.
The Fifer came though the ranks at Easter Road and picked up a League Cup winners medal before signing for the Parkhead club in 2007 for a reported £4.4million.
However, Scottish Cup success eluded him as it has Hibees players since a 1-0 win over the Hoops in 1902.
Brown was asked if he was aware of a desperation among the Hibs fans to end that hoodoo during his time at the Edinburgh club.
"Yes," he replied. "Every season it went on an extra year and it keeps going but hopefully it goes on another extra year for them, that's for sure.
"It is going to be a huge occasion for them. It is going to be a battle. "It is going to be hard for us and hard for them as well. It has been a long time since they won it but we want to get our hands on it as well."