Akhtar Ali also scored for the home side with all the goals coming in the latter stages of the match.
Bristol forward Rufus McNaught-Barrington, top scorer in the league,Â was denied twice early on by home keeper Maciej Pacanowski.
Havant took the lead in the 53rd minute after a ball was deflected off a defender into the circle. The unmarked Akhtar brilliantly pulled the ball down and tucked it under the keeper with a reverse shot to open the scoring.Â
University of Bristol followed with two good chances before levelling the score in the 61st minute.
Former Havant player Thomas Minall latched onto a ball that bounced through the defence to send it goal bound.
In the 64th minute Lewis Fraser was awarded a yellow card for an over robust challenge and the numerical advantage saw Havant take full advantage.
On 66 minutes Havant converted heavy pressure into a penalty corner, which pulled out two good saves from Bristol keeper Todd Dudley.
But the third shot from man-of-the-match Matt Cox struck a defender on the line and a penalty stroke was awarded.
Stubbings made no mistake after a well-placed flick into the side netting.
For the second time in as many weeks Havant faced a kicking back as University of Bristol replaced their keeper and within two minutes the move back fired on them.
Matt Cox won another penalty stroke when a defender stopped his goal bound shot with his body.
Stubbings produced a carbon copy flick past keeper DudleyÂ who had been substituted on to defend the stroke.
This win keeps Havant in fourth position in the table.
Havant ladies put their first three points on the board with a very good offensive first half and a very good defensive second half to beatÂ Hampstead & Westminster seconds 2-0.
Patrcja Hyla, Havant's player coach, scored in the opening minutes.
She then struck again midway throughÂ the first half to give Havant a 2-0 lead at the interval.Â
Hampstead & Westminster pressed heavily in the second half.
But Havant's resolute defending denied the away side any points.