Former England winger Tom Varndell said it was imperative to get the win over Worcester on Boxing Day.
Bristol edged closer to their wooden rivals when they beat Worcester, making the gap just two points on the overall table and Varndell, who scored a hat-trick, said it was vital that they got the win.
"Today, we knew it was all or nothing," said Varndell.
"If we had lost today, that gap between us and Worcester would have got bigger.
"We have had a good run in Europe the last couple of weeks, which has done wonders for our confidence. To win the way we did with 14 men is a massive credit to the whole team.
"We want to be in this league next year, and you have got to make winning a habit. We know what it is going to take.
"We could have fallen apart when Tusi was sent off, but the fans got behind us – there was so much passion out there – and the boys played for each other.
"It is a massive weight off our shoulders getting that first Premiership win. It has been long overdue, and hopefully now we can kick on."