Cyril Thereau volleyed home a perfect cross from Boukary Drame with one of the visitors’ only chances.
Roma, which had snatched a last-gasp win away at Fiorentina at the weekend, dominated but struggled to carve out scoring opportunities.
Its best chance came in the 53rd minute when Francesco Totti’s fierce 20-yard effort was deflected onto the crossbar.
Chievo goalkeeper Cristian Puggioni pulled off several saves to deny Mattia Destro, Totti and Pablo Daniel Osvaldo among others.
Roma remained provisionally fifth but can be leapfrogged by Udinese, which plays Palermo on Wednesday, while Lazio can draw level on points if it beats Inter Milan.
Chievo is now certain of avoiding relegation.
”We had an idea on how to approach the match, but did not pursue the ideas throughout the game,” said interim coach Aurelio Andreazzoli. ”In the first half we were stuttering in our build-up and should’ve tried to finish the game much earlier. In the final minute, we had this goal against the run of play.
”We didn’t suffer much at the back, but we knew that Chievo were dangerous on the counter.”