Tom Lowe gave the home side an early lead with a penalty goal, as Taffs Well took time to settle their nerves but a fine try by player-coach Steffan Edwards was just the tonic the side needed. Daryl Mota kicked the conversion for a 7-3 lead.
Lowe kept Rhiwbina close with his second penalty to leave his side 6-7 down at the break.
Mota , who was showing remarkable coolness for a player who had never kicked before, put over a penalty, and that was followed by a second try from Edwards, again converted by Mota, to increase the lead to 17-6.
Fullback Mike Baptiste then scored a fine solo try having run from deep in his own half. This was again converted by Moto, who had not missed a kick all afternoon.
But as Taffs Well ran from deep looking for their forth try and a bonus point, they were caught unawares and Richard Myers picked up the loose ball to score a consolation try for Rhiwbina.
Taffs Well's last two games are both against Pontyclun on Wednesday at home (kick off 7.15 ), and then on Saturday the return fixture at Pontyclun.