Inter, with only one win in their last seven league matches, were quickly in trouble when Alberto Paloschi fired the relegation-threatened Flying Donkeys ahead in the eighth minute.
Yuto Nagatomo levelled for Inter four minutes later, turning the ball in from close range after it was pulled back by Ricardo Alvarez, and the Japanese had a goal controversially disallowed for offside two minutes later.
Walter Mazzarri's team dominated possession for the rest of the game but struggled to create clear chances.
Inter are joint fifth, level with promoted Verona on 32 points from 19 games, 10 behind Napoli who are third in the Champions League playoff spot.
Three players were sent off as Sampdoria thumped Udinese 3-0 in Monday's other game.
Brazilian midfielder Allan was dismissed for Udinese in the 35th minute after two yellow cards in quick succession but the numbers were levelled up when Samp's Roberto Soriano was sent off just after the hour for a second bookable offence.
Udinese also had Allan's compatriot Gabriel Silva ordered off after he was booked for elbowing, his second yellow card.
Brazilian Eder gave Sampdoria a 16th-minute lead with a penalty and added another two minutes after halftime, although there was a suspicion of offside as he latched on to a flicked pass to score.
Daniele Gastaldello headed the third three minutes from time to leave Sampdoria 12th with 21 points and Udinese 15th with 20.