Chievo had an early opportunity but Alberto Paloschi smashed over from close range.
Maximiliano Moralez then gave Atalanta the lead, turning in the box and slotting into the bottom corner.
Giuseppe Sannino's team almost produced an instant response, but Cyril Thereau curled wide from 20 yards.
Marcelo Estigarribia had an even better chance to level the scores. Paloschi played the ball through to his teammate, but he hit his shot against the side-netting.
Sergio Pellissier volleyed wide for Chievo after being set by Palocshi, but the hosts struggled to break down their opponents.
Pellissier was denied a late equaliser when Andrea Consigli tipped his header onto the crossbar.
Simone Bentivoglio also went close, but his shot went just wide of the post.