Rolando Maran's men are chasing a Europa League spot but their failure to win at the Stadio Marc'Antonio Bentegodi means they are now three points behind fifth-placed Lazio, who host Juventus on Sunday.
In an even encounter, the visitors had the better opportunities to break the deadlock but a combination of poor finishing and Chievo goalkeeper Christian Puggioni making several fine saves proved their undoing.
It was Eugenio Corini's side, who are now eight points clear of the Serie A drop zone, that had the first sight on goal, with Perparim Hetemaj's low cross from the right narrowly just beyond the reach of Cyril Thereau.
The French forward then struck over the bar in the 20th minute as the hosts continued to pour forward.
But Catania nearly took the lead against the run of play when a quick counter-attack led to Alejandro Gomez teeing up Francesco Lodi, whose strike was parried away by Puggioni just before the half hour.
Lodi saw a free-kick sail harmlessly over the bar, while after the interval, the former Empoli midfielder picked out Gonzalo Bergessio with another set piece but the Argentinean forward's header at the far post saw brilliantly kept out by Puggioni.
Chievo reminded Catania of their potential, however, with Boukary Drame forcing Mariano Andujar into action from outside the area, while Sergio Pellissier fired over the bar on the hour.
But the visitors dominated in the closing stages and Bergessio only just failed to get any contact on Pablo Alvarez's low cross from the by-line.
Puggioni comfortably saved Mariano Izco's strike from the edge of the box while Alejandro Gomez failed to hit the target two minutes from time with his effort from distance as the spoils were shared.