Scarlets star Stoddart has been sidelined through injury all season but showed enough as a replacement he has lost none of his devastating power as an attacking force. He was still getting comfortable on the bench when Llanelli raced into the lead in the first minute when centre Scott Williams went over for a converted try.
Llanelli skipper Craig Hawkins and No 8 Ben Morgan added touchdowns for the visitors to race out to a 22-3 lead after 29 minutes.
The Wizards were reduced to 13 men when two of their pack were sin binned for technical offences and Llanelli were in no mood to let them off the hook as scrum half Gareth Davies was sent clear by Aaron Shingler to score the bonus point try.
After the break however, Aberavon were a different proposition. Flanker Chris Davies conjured a try and when Paul Bamsey collected a loose kick to score, suddenly it was 32-17 and the Wizards started to believe in themselves.
Justin Tipuric went over and when Bamsey scored to haul the Wizards within three points of Llanelli, nothing seemed impossible. In injury time Llanelli were struggling to hold on with two men in the bin.
Aberavong were given an 86th-minute penalty in front of the Llanelli posts and Murphy tidied up, leaving both sides with three points.
Scorers: Aberavon: Tries – P Bamsey (2), C Davies, J Tipuric; cons – J Murphy (2), M Jarvis; pens – M Jarvis, J Murphy
Llanelli: Tries – S Williams, C Hawkins, B Morgan, G Davies; cons – D Newton (3); pens – D Newton (2)