Inter played like a Mourinho team, full of power, commitment, organisation and a little swagger too.
The only negative for Mourinho was injuries to two centre-backs as both Marco Materazzi and Nicolas Burdisso left the game during the first period.
That and United's impressive showing in beating Fulham in the FA Cup will be Mourinho's two main worries ahead of Wednesday's Champions League last 16 clash at Old Trafford which is finely balanced at 0-0 after the first leg.
This win was the perfect response to Inter's midweek 3-0 Coppa Italia defeat to Sampdoria.
"What happened against Sampdoria was due to individual mistakes, which can
happen in football," said Mourinho.
"Tonight we played with great spirit. After losing Materazzi and Burdisso we had some problems with our formation. Ibrahimovic wanted to come off but other players like Balotelli were fantastic. They weren't easy opponents."
Inter got off to a wonderful start with Dejan Stankovic playing in Ibrahimovic in the second minute and the big Sweden forward holding off two challenges before chipping Genoa goalkeeper Rubinho for his 15th goal of the season.
Genoa had a real go at Inter in the first 45 minutes and Brazilian goalkeeper Julio Cesar twice had to save the champions with excellent saves from Thiago Motta and Giuseppe Biava.
Any chance the hosts had of getting back into this game ended just past the hour mark as teenage forward Balotelli added the second, although there was a doubt as to whether or not the ball actually crossed the line.
Earlier, 10-man AS Roma missed the chance to move into the top four as they were held to a 1-1 home draw by Udinese.
They are now level on 45 points with Genoa but crucially one point behind
fourth-placed Fiorentina, who host Palermo on Sunday.
Roma were lucky to escape with a point after Udinese were denied a first half penalty while the hosts had to survive the last quarter of the game with a numerical disadvantage following the dismissal of Daniele De Rossi.
Brazilian Felipe had given Udinese the lead nine minutes into the second period but substitute Mirko Vucinic rescued a point for Roma just past the hour mark.
The capital-based team possibly had one eye on next week's Champions League second leg clash against Arsenal - in which they trail 1-0 from the first leg in London - because they failed to play with any spark throughout a largely dull match.
The most controversial moment came right at the end of the first half as Switzerland midfielder Gokhan Inler burst into the Roma box only for France defender Philippe Mexes to apparently handle the ball.
However, the referee waved play on.
Justice seemed to be served on 54 minutes when Antonio Di Natale crossed for the unmarked Felipe to score easily with a header at the back post.
Roma coach Luciano Spalletti threw Vucinic into the fray and he ran unchallenged across the Udinese box before shooting home right-footed to restore parity.
De Rossi then got his marching orders after arguing with the referee.