Argentine forward Diego Milito set the champions on their way with a diagonal strike on ten minutes. They spent long periods under intense pressure in their own half after Dutch playmaker Wesley Sneijder was sent off for dissent in the 27th minute before Goran Pandev doubled the lead with a free kick in the 65th.
Inter keeper Julio Cesar saved a generous stoppage-time Ronaldinho penalty for handball by Lucio, who also saw red.
In other matches, Abel Hernandez hit the headlines by scoring twice along with Igor Budan to help Palermo to a 3-0 win over Fiorentina yesterday that took the Sicilian side up to fifth.
Juventus, who lost 2-1 at home to AS Roma on Saturday, have now slipped to sixth place
In Germany's Bundesliga, the future of VfL Wolfsburg coach Armin Veh hung in the balance after the champions lost 3-2 at home to lowly Cologne yesterday. Wolfsburg are a shadow of the team who romped to their maiden title last year, losing their last three league matches and failing to win since early November.
Elsewhere in the top flight, Bayer Leverkusen reclaimed top spot with a 3-0 victory at Hoffenheim.
Leverkusen remain the only undefeated team in the league.
In Holland, Dutch club PSV Eindhoven say they have sacked Brazilian forward Jonathan Reis after he used "banned substances." The club did not identify the substances, saying only in a statement
that it had recommended Reis attend a clinic to "quit this problem" but he refused. The club then decided to fire him with immediate effect.