Jake Livermore's first Hull goal set the home side on their way but Steven Gerrard's superb free-kick levelled the game at half-time.
Despite this setback, the hosts grabbed a deserved win with a stirring second-half performance that saw David Meyler score his first of the season with a composed finish and Martin Skrtel's late own goal secure the result.
The triumph was Hull's first over Liverpool in their history and though Bruce was understandably delighted, he also urged his team to build on their solid start.
He said: "I thought we were marvellous today. We've played extremely well, especially after the disappointment of last week. We've won five and find ourselves in the top half of the table.
"I think you need 10 wins to stay up, so to have five at this point is encouraging. We can't rest on the start we've made though."
Hull had lost four of their previous five games but Sunday's win - which puts them 10th in the league - means they have lost just once in seven league outings at the KC Stadium this season and Bruce believes it will give his players great confidence.
He added: "The results like today give some of these players, some of whom have not played in the Premier League confidence that they can go and beat teams like Liverpool."
The Hull manager was also full of praise for goalkeeper Allan McGregor, who made a crucial save from Victor Moses a minute before Meyler put Hull ahead for the second time.
"McGregor has been fantastic for us this season and I'm delighted with him," Bruce enthused.
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