The home side had actually started the better and moved into an early lead with Josh Prosser searing through a gap to cross the line. The conversion went wide and Bedwas soon hit back with Richard Powell kicking two penalties to put them into the lead for the first time.
Despite moving ahead, Bedwas were struggling to break down an organised Bargoed defence but before half time, there was still time for each side to score a try apiece. First, Kyle Maiden strolled over for Bedwas then Prosser added his and Bargoed's second when he swallowed up a loose pass. Both conversions were added to bring to an end a tight first period.
On a heavy pitch, the second half became a war of attrition. Prosser and Powell exchanged further penalties and both teams flooded the pitch with replacements in search of the winning score.
It was Bargoed who had to do all the chasing though and with less than five minutes remaining, they had a chance to win it. Prosser eyed up a long range penalty but saw his kick fall short as Bedwas progressed to the next round.
Steve Law's side now face a home tie with Cross Keys in round two on Saturday, February 15.