Inter, looking for only their second win in seven games, were stunned after just eight minutes when Alberto Paloschi was left unmarked in the area to beat Samir Handanovic with a dipping shot. Walter Mazzarri's men were soon back on level terms, Yuto Nagatomo leaving Chievo's static defence behind to meet Ricardo Alvarez's pass across the face of goal and beat Christian Puggioni in the Chievo net on 12 minutes.
Nagatomo had the ball in the net for the second time less than a minute later after first-timing Jonathan's drive past Puggioni, however Rodrigo Palacio had strayed offside to the right of goal. Inter dominated the remainder of the encounter but despite a second-half substitute appearance from Argentinian striker Diego Milito the Nerazzurri failed to break down a stubborn Chievo defence.
Inter's eighth draw moved them up one place to fifth but sit 20 points adrift of leaders Juventus and ten behind Napoli in the third and final UEFA Champions League qualifying spot.
Earlier, Sampdoria continued their promising run under new coach Sinisa Mihajlovic to move two places up to 12th. Brazilian striker Eder struck twice for the hosts, opening the scoring from the spot in the 16th minute after he had been felled by Udinese 'keeper Ivan Kelava's sliding tackle.
Eder was a thorn in Udinese's side all night and when Brazilian midfielder Allan was cautioned for a second time for fouling his compatriot he saw red on 35 minutes. Eder doubled Sampdoria's lead two minutes after the restart after scoring from Manolo Gabbiadini's backheel flick.
Sampdoria found themselves reduced to 10 men when Roberto Soriano picked up a second caution for a foul on Maurizio Domizzi. But the hosts regained numerical superiority shortly after when Gabriel Silva was given his marching orders on 69 minutes for jumping with his elbow up on Lorenzo De Silvestri.
Eder came close to a hat-trick when a superb curling effort sailed just over. When Samp's third goal came, it was from the most unexpected source, Daniele Gastaldello claiming his first goal in over a year with a glancing header from a free kick which beat Kelava at his far top corner.