Matthew John, Dean Gunter and Matthew Pewtner also went over but the home side didn't have it all their own way in what was a game of two halves.
With Richard Powell out injured and Ethan Davies attending Wales U20 training, Bedwas bought in Gunter, on permit from Cross Keys, to start at fly half.
Aberavon arrived at Bedwas with just the one win so far this season but they caught the home side cold, taking the lead with less than two minutes on the clock. Sam Williams charged through several tackles and crossed for a try. Craig Evans converted and the Wizards were off to a fast start. They then doubled their lead five minutes later with a score out wide from Stef Andrews, Evans again converted to leave Bedwas facing an uphill battle.
The home side were struggling to get out of their own half such was Aberavon's stranglehold on the game, and even when the visitors went down to 14 men following Ben Thomas' sin binning, Bedwas could not use the extra man to assert any pressure. When they did have possession, they made too many unforced errors and could not build any momentum.
Towards the end of the half it was all Aberavon but Bedwas defended resolutely to repel wave after wave of attack.
Budina then got Bedwas back into things with his first score. Stuart Thomas took a quick tap and sprinted 50 metres before releasing the winger to score under the sticks. Gunter added the conversion with the last kick of the half.
With the wind at their backs for the second half, it took Budina less than 90 seconds to run in his second try after Bedwas moved the ball wide. Gunter was unsuccessful with the conversion.
The score saw Bedwas grow in confidence and John soon added a further score. Gunter converted and following another blistering attack, the fly half crossed for a score himself.
Aberavon were now struggling to find an answer to Bedwas' incisive back play and a try from Pewtner and a third for Budina meant that Bedwas had scored 38 unanswered points to put the game beyond doubt.
The Wizards refused to give up though and the two Gareth's, Harvey and Ronan, both went over for tries with a Gunter penalty sandwiched between the two.