His sixth-minute equaliser against the Teessiders on Saturday sparked a recovery which was once again completed deep into injury time as substitute Daryl Murphy claimed the last-gasp winner which not only secured the points, but confirmed the club's presence in the top flight next season.
Higginbotham said: "It is a huge club, there's no doubting it. When you are getting 45,000, 46,000 at home - and when they are behind you like they were today - it is magnificent.
"I don't think it is any coincidence the amount of late goals we do score here because the fans are 110 per cent behind us.
"This club is where it deserves to be, in the Premier League, and each year, it is going to get stronger and stronger."
Sunderland arrived back in the top flight with big ambitions as Keane insisted they were not returning simply to make up the numbers.
He has since invested around £44million of the Drumaville consortium's cash in an effort to make the impact for which he hoped, and while the season has proved intensely difficult, there was a sense of achievement on Wearside on Saturday evening.
Higginbotham said: "It would have been nice to have been a little bit more comfortable, but we have done it with two games to spare.
"It's a great achievement and everybody is delighted - but we cannot sit back and rest on our laurels now.
"The aim is to finish the season as strongly as possible. We owe it to the fans and everybody to finish as strongly as possible."