Akhtar Ali andÂ Charlie Stubbings got the goals for the Barncroft Way side to give them an excellent three points.
Havant had to hold their nerve under pressure late in the match to seal a well-deserved win and move up to third position in the table with 15 points from seven matches.
The game started brightly for both teams, although neither were able to create any clear cut chances.
Bath had the better of the early exchanges but could not troubleÂ Maciej Pacanowski in the Havant goal.
Havant were soon in the game with some good work from Miguel Rodrigues who fed the ball to Charlie Stubbings who won Havant's first penalty corner.
UnfortunatelyÂ the routine broke down at the top of the circle and the chance went begging. Bath soon won their own penalty corner in the 14th minuteÂ but this was charged down by Havant's skipper Craig Duffy.
Havant's midfield created a great chance for MattÂ CoxÂ but his reverse stick shot was well saved by the Bath goalkeeper. It was not until the 28th minute when Havant took a deserved lead.
Havant attacked down the right with Ethan Hoddle, whose cross found Akhtar at the top ofÂ the circle.
Akhtar turned his defender and drilled his shot into the net. The halfÂ finished with a 1-0 lead for Havant and coach Raj Laly was refocusing his team ready for the inevitable response from Bath.
It was not until the 61st minute until Havant won their second penalty corner.
Federico Bertoni's flick hitting the postman's foot on the line and a penalty stroke wasÂ awarded.
Charlie Stubbings having converted two penalties last week, calmly stepped up and made no mistake to give Havant a two-goal lead.
Bath withdrew their goalkeeper to try and get back into the gameÂ but Havant's defence held firm.
However in the 68th minute, Bath did get a lifeline with a far-postÂ tap in.
But Havant held out to wrap up the victory.
Meanwhile, Fareham earned a good 4-3 win at Chichester.
Jack Gilbert scored twice and Niall Stott also netted a double.
On Sunday Fareham host Cardiff & Met at Henry Cort (1.30pm).