Strikers Jordan Davies and Ben Fawcett both netted braces, with Jack Wilson and Jamie Veale adding to the tally late on to give the Bluebirds a comfortable win at Parc Ynysderw.
It was the hosts who had the first opportunity of the game when a header at the back post from a free-kick went just over the bar.
The remainder of the first-half belonged to Haverfordwest County though, as the Bluebirds created numerous chances.
Fawcett’s ball across the face of goal picked out his strike partner Davies, but he couldn’t direct his effort on goal. Ioan Evans then fired a shot over the bar shortly after, but it didn’t take long for the Bluebirds to find the opening goal.
A pinpoint pass from midfield played Jordan Davies in, and he took the ball around the goalkeeper before rolling it into an empty net to make it 1-0.
Tony Pennock’s side found a second goal just eight minutes later when, from an attack that started with goalkeeper Zac Jones, the ball was worked to Rhys Abbruzzese, and the wing-back squared to Jordan Davies who shot first-time into the right corner for his second goal of the night.
County made it three goals in 11 first-half minutes when they won the ball back high up the pitch, allowing Fawcett to get a strike away from the edge of the area which found the net to extend the lead to 3-0.
Just after Jordan Davies had been a denied his hat-trick by the offside flag, Jones did well to get a hand to a shot from range to ensure our advantage remained at three heading into half-time.
The hosts, who will be playing in the second tier JD Cymru South in the upcoming season, competed well throughout the first-half and made life difficult at times for the Bluebirds, but Pennock’s side began to take real command after the break.
It was very nearly 4-0 just three minutes into the second-half when Ryan George went on a brilliant solo run into the penalty area before seeing his curling effort hit the stanchion and go behind. Jordan Davies then saw his shot from inside the area saved low down, but three minutes later the fourth goal arrived.
After haring down the right wing, George crossed into the area to find an unmarked Fawcett who tapped in from point-blank range for 4-0.
It was very nearly 5-0 less than five minutes later, as Evans’ excellent through ball played Jordan Davies in, but his shot came back off the left post.
The chances continued to come for County, who were in total control at this stage, and the fifth goal came when Abbruzzese chipped the ball into the area for substitute Jack Wilson to head in from close range.
Pontardawe were awarded a penalty with just over 15 minutes remaining for a pull inside the area, and Ryan Kostromin converted from the spot to make it 5-1.
Haverfordwest County: Z. Jones, George, L. Davies, Jenkins, Humphreys, Abbruzzese, Evans, Watts, Veale, J. Davies, Fawcett
Substitutes: Brass, D. Rees, T. Davies, Trialist