The Nerazzurri have now lost three of their last four games, a run which has all but ended their Serie A title hopes and also placed a serious question mark against their chances of qualifying for the Champions League.
Andrea Caracciolo scored the only goal of the game in the 56th minute as Novara completed the double over Inter this season.
They even held onto the win after Ivan Radovanovic was sent off with 10 minutes to go.
Inter owner Massimo Moratti was forced to issue a statement on Thursday denying the club were considering dismissing Ranieri and replacing him with former England boss Fabio Capello.
But this setback leaves Ranieri's side fifth in the table, five points behind fourth-placed Udinese and 11 adrift of leaders AC Milan.
Pablo Barrientos scored twice as Catania claimed their first win of 2012 in style with a 4-0 thrashing of Genoa.
The visitors went into the game on the back of two straight wins but found themselves a goal down after just seven minutes through Francesco Lodi's penalty.
Barrientos then netted a quickfire double in the 49th and 52nd minutes, before Gonzalo Bergessio rounded off the scoring 10 minutes later.
Atalanta hit the post twice but their problems in front of goal continued as they were held to a goalless draw by Lecce.
The Bergamaschi were the better side at the Stadio Atleti Azzurri d'Italia but could not find a way past Lecce goalkeeper Julio Sergio, although both Guido Marilungo and Federico Peluso struck the woodwork.
The result left Atalanta in 15th place, six points clear of third-bottom Lecce.
The matches between Bologna and second-placed Juventus and Parma and Fiorentina were postponed due to bad weather.
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