While Roma won 2-0 away at Chievo, Inter secured their victory thanks to Diego Milito's second-half goal.
Chievo had plenty of chances to at least level, with Sergio Pellissier having excellent opportunities in each half.
Mensah has also had spells in Italian football with Modena, Chievo and Genoa, as well as Rennes in France.
Instead it was Chievo who scored the game's second and final goal -- Boukary Drame netting in the 76th-minute.
In Italy's Serie A , fourth-placed Udinese's Champions League hopes were dented by a 0-0 draw with mid-table Chievo on Saturday.
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Numerous others have had their houses searched, including Chievo Verona's Sergio Pellissier.
In Italy's Serie A, defending champions Juventus maintained their 100 per cent start to the season with a 2-0 win over Chievo.
Juve's day got better when second placed Napoli went down 2-0 at Chievo Verona after goals from Boukary Drame and Cyril Thereau.
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The victory lifted them one point clear of AC Milan, who had briefly gone top with a 1-0 win at Chievo Tuesday.
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In Serie A's other Saturday fixture, Chievo drew 1-1 with relegation-threatened Palermo.
In Italy, Roma missed the chance to draw level on points with fifth-placed Fiorentina in Serie A after they lost to Chievo Verona.
Elsewhere, Udinese eased to a 3-0 win at Parma, while Palermo finished 1-1 against Bologna, Chievo finished goalless against Catania and Genoa drew 1-1 with Sampdoria.
Elsewhere, Fiorentina gained a 2-1 win over Chievo, Bolgona defeated Cagliari 3-0 and Emanuel Icardi's 58th minute effort secured all three points for Sampdoria against Parma.
Thiago Silva added a fourth in the 58th minute to keep the reigning champions ahead of second-placed Juventus who dropped points at home to Chievo .
The result means city rivals AC Milan will cut their advantage at the top of the table to a single point if they defeat Chievo on Sunday.
Meanwhile, Juventus slumped to their seventh defeat in 10-games with a 1-0 reverse at Chievo that is sure to increase the pressure on under-fire coach Ciro Ferrara.
Elsewhere, AC Milan claimed a 2-1 win over Siena thanks to goals from Bojan and Giampaolo Pazzini, while there were also wins for Chievo, Genoa and Parma.
Beckham, who is on loan with AC Milan in Italy from the Los Angeles Galaxy, limped off during the Serie A side's home match against Chievo on Sunday.
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Third-placed Lazio could have cut Juve's then five-point lead to two in Saturday's earlier game, but lost 1-0 to midtable Chievo to stay below Napoli on goal difference.
Having suffered a shock home defeat against Siena on Sunday, Inter responded by moving up to fourth after winning 2-0 at Chievo, thanks to goals from Alvaro Pereira and Antonio Cassano.
In Italy , Juventus moved three points clear at the top of Serie A with a 2-1 win at Chievo but the big story of the day was Balotelli's controversial debut for AC Milan.
But Milan's performances in the Italian league, with Beckham playing his part, have been more impressive and Sunday's eventual 1-0 win over Chievo left them hot on the heels of arch-rivals and defending champions Inter Milan in the title race.
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