Boyle's shot from the right side hit Ellis, but had enough momentum left to trickle into the net and snap a 3-3 deadlock at 19:00 of the third period.
Setoguchi had tied the game at 13:26 of the final period with an assist from Boyle, after Patric Hornqvist had staked the Preds to a 3-2 lead earlier in the period.
Michael Santorelli and Marcel Goc had Nashville's earlier goals. Ellis made 25 saves in the loss.
San Jose goalie Thomas Greiss faced 26 shots and allowed three goals.