Gonzalo Bergessio put the home team in front but Francesco Modesto equalised 10 minutes later.
Neither side had the courage to seek a win in the second half, although Stefano Okaka almost grabbed a winner on his Parma debut in the last minute.
In the first game since the sale of Maxi Lopez to AC Milan, Pablo Barrientos and Bergessio were given a chance to show they have what it takes to lead the line for Catania.
Barrientos had a good chance to open the scoring when he volleyed just over the crossbar in the third minute, but Bergessio went one better with his first chance, opening the scoring in the 33rd minute after being put through by Marco Biagianti.
He seemed to have let the chance slip as he nudged the ball past the Parma goalkeeper and seemed to go too wide, but he cut his shot back between two defenders and into the far corner.
Parma's reaction was swift with Sergio Floccari heading against the base of the right post in the 43rd minute.
Catania failed to clear the ball sufficiently as Parma remained on the attack and the ball fell to Modesto, 20 yards from goal, and his shot managed to filter through two Catania defenders on its way into the bottom corner.
Catania started the second half as they started the first, with Francesco Lodi sending one of his trademark free-kicks just wide of the far post.
Parma almost stole the points in the 90th minute when debutant Okaka used his pace and strength to enter into the penalty area, but he shot wide of the far post with only the goalkeeper to beat.