Nardiello took his remarkable tally to six goals in four games before leaving ten minutes from the end to a standing ovation from grateful Oakwell fans.
Nardiello produced a wonderful opener after 16 minutes, but his second from the penalty spot after 68 minutes was shrouded in controversy.
Nardiello almost caught out the Palace defence in the opening seconds and then after nine minutes produce a looping shot that drifted just wide of the upright.
As Palace responded, Carl Fletcher pounced on to a half-cleared corner at the other end, but his hasty effort was over the top and when Shefki Kuqi hit a wild shot it failed to trouble home keeper Nick Colgan.
It was Nardiello who broke the deadlock after 16 minutes with a wonderful solo effort to claim his fifth goal in four games.
He collected the ball from Martin Devaney and flashed his impressive footwork to skip round three defenders to create space and exploit it with a superb shot that had a slight deflection to help it past Julian Speroni.
Nardiello might have added a second with a brilliant solo run nine minutes into the second half, but as he burst into the area the ball ran to Istvan Ferenczi who was offside.
And when Devaney raced down the right he saw his low angled shot easily saved.
Palace, though, produced a stirring second-half fightback that had Barnsley scrapping for their Championship lives.
Nardiello was in the thick of it as the visitors chalked up 11 corners as he cleared off the line when Leon Cort powered in a goalbound header.
But Barnsley claimed a controversial second after 68 minutes when Nardiello burst into the area and was chopped down by Matt Lawrence.
Barnsley were denied the goal when Speroni saved Nardiello's tame spot-kick, but the linesman immediately flagged that the keeper moved forward and Nardiello made no mistake with the second attempt.
In the aftermath as Palace protested, substitute keeper Gabor Kiraly was yellow carded for his comments.