The hosts looked on their way to a memorable victory when they went four up thanks to Hernan Crespo's brace and efforts from Walter Samuel and Dejan Stankovic, with just 13 minutes remaining on the clock.
However, Sergio Pellissier, Simone Tiribocchi and Matteo Brighi scored back-to-back goals and almost secured a point out of the blue but the final whistle rescued Inter from a stunning draw.
Inter's defense repeated the slips it made during Fiorentina game when the team were enjoying a three-goal lead before conceding twice in the closing stages of the game.
Roberto Mancini's side top the league table with 10 points from four games while Chievo are 16th with only one point.
Crespo registered Inter's only goal in the first-half in the 11th minute when he ghosted past the back four and sent a superb finish home.
The floodgates opened after the break with Samuel heading home after a poor clearance from goalkeeper Lorenzo Squizzi in the 57th minute.
Four minutes past the hour mark, Stankovic drilled a trademark shot from outside the area to make it three before Crespo netted his second goal of the game six minutes later after a neat assist from Adriano.
Chievo ran riot starting from the 77th minute when Pellissier pulled one back from the spot after being downed in the area by keeper Julio Cesar.
Tiribocchi's 86th-minute long-range shot sparked the visitors into life before Brighi narrowed the gap even more with the third goal one minute later.
But Inter held on to the slim lead in the remaining minutes to secure the precious points.
Elsewhere, Roma kept Inter in sight with a crushing 4-0 away triumph over Parma.
Vincenzo Montella broke the deadlock as early as the fifth minute and Simone Perrotta send the visitors to the locker room with a two-goal lead after adding the second on the stroke of half-time.
Nineteen-year-old midfielder Aleandro Rosi poked home in the 54th minute and Alberto Aquilani put the icing on the cake in the dying seconds.