The Nerazzurri went into the contest looking for their first win in 2014 and had their chances but lacked a finishing touch.
The closest Inter came to taking three points was seven minutes from time when Rolando's header was kept out by Catania goalkeeper Alberto Frison.
The result may have extended Inter's winless run to five games but the point has at least allowed the Nerazzurri to remain in fifth place, where they are one point clear of Torino, Parma and Hellas Verona.
Catania, meanwhile, failed to test Inter goalkeeper Samir Handanovic for the entire match and remain at the foot of the standings, four points from safety.
Inter have struggled to score of late, with just one goal arriving in their previous four games.
Despite facing the leakiest defence in the competition, Inter had to wait until the 26th minute to test Frison.
Diego Milito's powerful effort from outside the area forced the visiting keeper to clear at full stretch.
Soon afterwards, Rodrigo Palacio found space in Catania's box and struck a right-footed shot that went too high.
Before half-time, Esteban Cambiasso saw Frison off his line but his attempted lob ended up in the stands.
Catania came to life in the second half and in the 48th minute Gonzalo Bergessio's left-footed shot from the edge of the area went just wide of the far post.
Fabian Rinaudo came closest for the visitors but his attempt from outside the box went just over the bar.
In the 75th minute, Alvarez's free-kick went straight into the wall as Inter wasted yet another good opportunity.
Catania almost shot themselves in the foot when they failed to clear a dangerous ball into the area in the 83rd minute, but Frison saved Rolando's goal-bound attempt.
Inter still had a chance to earn all three points but Palacio nodded Alvarez' free-kick over the bar.