Losing 19-3 after 80 minutes, the home side scored two converted tries in a remarkable 13 minutes of injury time that gave the visiting faithful a fright.
The Wizards made the perfect start when left wing Chris Lewis scored in the corner just two minutes into the game after some great work by the Aberavon flankers.
Cardiff fly half Scott Sneddon had a chance to reduce the deficit not long afterwards but missed with his penalty kick. Opposite number Matthew Jarvis also missed with a long range penalty attempt coming up to the end of the first quarter, while Sneddon hit the post after half hour to leave the score at 5-0 at the interval.
A Jarvis penalty early in the second half was cancelled out by Sneddon as he got the first points on the board for the homeside.
Jarvis kicked his second penalty of the afternoon to make the score 11-3 to the Wizards at the end of the third quarter.
In the last 10 minutes of normal time Jarvis increased the visitors lead with a third penalty kick. In the 80th minute wing Lewis scored again in the corner to give the Wizards a 16 point lead.
However, referee James Jones surprised both sets of supporters by playing 13 minutes of injury time that saw Cardiff hit back with two converted tries. First replacement Sion Hopkins scored and then centre Richard Smith. Sneddon converted both to leave the Wizards fans with a nervous couple of minutes before the final whistle.