The Japan international equalized just four minutes after the visitors' shock opener but Walter Mazzarri's side have now gone three games without a win in 2014.
Alberto Paloschi handed the visitors a surprise lead after Boukary Drame's cross caused havoc for Juan Jesus and Hugo Campagnaro, allowing the forward to rifle home into the top corner.
Inter restored parity within five minutes, however, as Yuto Nagatomo swept home Ricky Alvarez's low cross, but Walter Mazzarri's side failed to find a winner, meaning it only scrapes back into Serie A's top five ahead of Hellas Verona.
The draw lifts Chievo a place in the table and means it is now a point clear of the relegation zone at the halfway stage.
Both sides made two changes from their previous league outings, with Inter welcoming back Mateo Kovacic in place of the suspended Fredy Guarin and the visitors opting for Paloschi in attack instead of Sergio Pellissier.
Despite only taking one point from a possible 12 the visitors started well and broke the deadlock early.
A move down the left ended with Campagnaro and Juan Jesus colliding in the Inter defense, the loose ball rolled to Paloschi inside the penalty area, and he fired high above Samir Handanovic and into the back of the net from a tight angle.
Inter hits back almost immediately with a well-worked goal that Nagatomo converted from close range.
Alvarez teased Perparim Hetemaj on the right before delivering a low cross into the six-yard box that the Japan international swept home.
Mazzarri's side should have gone into the break ahead, but it saw another Nagatomo effort disallowed for offside, while Rodrigo Palacio and Alvarez both failed to force Christian Puggioni into a save with their chances.
Inter started the second half positively but was wasteful in attack as Kovacic, Alvarez and Rodrigo Palacio all spurned chances to put it ahead.
The latter came closest with a scooped effort following Alvarez's through ball, but the 31-year-old saw his chance loop onto the top of the goal with Puggioni untroubled.
Chievo did create an opportunity of its own in the 71st minute as Cyril Thereau and Paloschi broke on the counterattack. The French striker was played in by his teammate but dragged his shot well wide of Handanovic's goal.
Inter continued to press for a winner but failed to find a way past its resilient hosts, meaning they extend their winless run in 2014.