She opened the scoring from a penalty flick after the ball was stopped on the line by a Havant defenders.
Puckett added a second before half-time and, after she had completed her treble after the restart, Danni Francis’ quickfire double extended the lead to 5-0.
Solid midfield play by Carol Rutter and Amy Rook broke down Havant's attacks, while debutant Olivia Harridine impressed going forward.
Havant hit back with a well executed short corner but Rook completed the scoring.
Portsmouth’s women’s 2nds suffered a home defeat against Basingstoke 3rds in South Central Division 2 South.
Two first half goals condemned the side - who had Pete Tunstall available to coach them - to a 2-0 loss at Admiral Lord Nelson School.
The side’s new formation worked well in the second half with player of the match Chloe-Jeane Parsley and Joni Duffus holding the central Basingstoke players at bay and Clair Hamson distributing the ball out to Hayley Chivers, Katie Allard and Lucy Dunning on the wings.
Portsmouth held strong as Basingstoke attacked with good defending from Katie Davey, Emily Dunkason, Duffus and skipper Emily Crowcroft.
Gen Wibberley’s leveller enabled Portsmouth 4ths to enter half-time level with Chichester 4ths in Division 2 Solent.
Keeper Kirsty Harley produced a string of fine saves in the second half but Chichester still netted three more times to seal a 4-1 win.
Portsmouth have folded their women’s 6th XI.