Cooper's second came a minute later and what a goal it was. Starting from a long throw from City's keeper Tom Pamment, the ball found Nathan Farey who made a strong run up the right hand side before firing a cross for Cooper to put away.
The visitors could have been up 4-0 at the break had it not been for a missed Hughes penalty, with the fourth eventually coming in the 68th minute when Hughes, put through by a superb ball from Roach, weaved his way through the Claudelands defence before placing a shot wide of the keeper.
Cooper's third came again from a Hughes pass, giving him his first hat-trick of the season.
The game was effectively over then so coach Duncan Lowry took the opportunity to replace Cooper and Hughes with Jack Chaney and Will Clague respectively.
It was a commanding win by the Blues, who totally dominated the match, leaving only a few scraps for the home side who rarely threatened the visitors' goal.
Tauranga now sit three points clear on the table, helped by a loss suffered by second-placed Waiuku, who went down 4-3 away to Onehunga Mangere.
The Blues next match is against Onehunga Mangere at Links Avenue on Sunday
Tauranga City United 5 (Jordan Culpepper, Andrew Cooper 3, Jerahl Hughes) Claudelands Rovers 0.