After kicking off its journey in the Italian league with a 1-0 away win over Bologna, SPAL notched its second consecutive win on Sunday to hold the third position in the Serie A table with six points.
Both SPAL and Parma failed to open the scoring in the first half, but Antenucci netted the lone goal just four minutes into the second half.
Antenucci connected with a stunning volley off a cross to give the Parma keeper no chance as he scored the only goal of the game.
Parma, which was held to a 2-2 draw with Udinese at home in the Serie A opener, fought to score the equalizer, but SPAL managed to secure the win and earn the three points for the game.
After the away defeat, Parma is provisionally in the ninth position with a single point.
Defending champion Juventus, which defeated Lazio 2-0 on Saturday, leads the table with six points, on goal differential ahead of second-placed Napoli.