Walter Samuel caught Nicola Pozzi with his arm as the last man and was given a straight red card on the half-hour before Ivan Cordoba picked up a second yellow for a foul on the striker after 39 minutes.
Despite the advantage, fourth-placed Samp failed to impose themselves and relentless Inter carved out the best chances for Samuel Eto'o and Wesley Sneijder in their third successive draw.
More controversy came when Cameroon striker Eto'o, returning to the lineup but not assured of a start against Chelsea, was booked for diving in the area in the second half.
RARE PROTEST
Mourinho, who has now not lost in 130 domestic home league games over eight years at Porto, Chelsea and Inter, burst out laughing at that point while the San Siro crowd waved white tissues at the referee in a protest rarely seen in Italy.
Samp then had Giampaolo Pazzini dismissed for two bookings to effectively end their hopes of extending their four-game winning streak and doing the double over the Italian champions.
Inter midfielder Dejan Stankovic returned from a month out while Javier Zanetti played at left back with Davide Santon injured and looks poised to retain the role on Wednesday.
Seventh-placed Genoa are just two points behind city rivals Samp, who now have 40 points, in the fourth Champions League qualifying spot following an easy 3-0 home win over Udinese in Saturday's early game.
Striker Robert Acquafresca grabbed the opener on the rebound after half an hour and then won and converted a penalty early in the second half.
Udinese defender Cristian Zapata was sent off for a second booking before Rodrigo Palacio turned in a third to leave the visitors just a point above the drop zone.
