Milan captain Riccardo Montolivo was sent off seven minutes from time before Sergio Pellisier saw red for the visitors in injury-time.
Robinho struck a post and Alessandro Matri went close for Milan in the second half but the stalemate means Massimiliano Allegri's side are now without a win in six games in all competitions.
The hosts were unchanged from last week's draw at Bologna, while Allegri made just one alteration from the side that lost in Barcelona in midweek as Alessandro Matri returned to the front line in place of Robinho.
After a quiet opening, Chievo were first to threaten in the 17th minute as Marcelo Estigarribia stung the palms of Christian Abbiati from 25 yards, before Bostjan Cesar fired wide when well placed following the resulting corner.
Milan's response was immediate, though, as home keeper Christian Puggioni had to move low to his left to smother Sulley Muntari's effort from distance after a surging run from the Ghanaian.
With chances at a premium in a scrappy first half, Andrea Poli wasted a good opportunity to break the deadlock for Milan three minutes before the break when he dragged his shot wide after being found by Matri inside the area.
Six minutes after the restart, the hosts spurned a golden opportunity to open the scoring.
Cyril Thereau's shot was parried by Abbiati and the rebound ran perfectly for Rigoni, who, from a slight angle, hit the side netting when presented with an open goal six yards out.
Puggioni was called into serious action for the first time on the hour mark. The goalkeeper beat away Urby Emanuelson's swerving long-range effort before diving full length to his left to keep out Philippe Mexes' volley from 20 yards.
The hosts had a goal disallowed for offside with 16 minutes remaining when Thereau poked the ball beyond Abbiati but the linesman had raised his flag, with replays suggesting he may have just been level with the last defender.
Once again Milan's response was swift, Poli firing wide from the edge of the area, before Robinho missed Milan's best chance of the game, as he struck the base of the post from 12 yards after being played in by Muntari.
Three minutes later Montolivo was dismissed for a second bookable offence after a challenge from behind on Perparim Hetemaj.
Despite their temporary numerical advantage, Matri fired another good chance wide a minute later before Pellissier saw red as Milan - and Allegri's - troubled season continued.