Diaby struck either side of half-time to ensure the triumph over the Serie A champions, and now has three goals in his first four games since his move from Aston Villa.
The defeat is Inter's first of pre-season, with Simone Inzaghi's side concluding their preparations for the new season against Chelsea this weekend.
Having been second-best in the opening exchanges, Al Ittihad took the lead in the 25th minute when Diaby was picked out by Houssem Aouar before firing the ball beyond
Yann Sommer.
Despite Inter registering seven shots to their opponents' four in the first half, they found themselves further behind two minutes into the second half.
A loose pass by Alessandro Bastoni was punished as Ahmed Al Ghamdi saw his effort saved by Sommer, only for the rebound to fall kindly for Diaby to score his second.
Milan improved in the forward areas but were unable to test Predrag Rajkovic as Laurent Blanc's side held on for the win in Italy.
Data Debrief: Diaby does the business
After scoring six times in the Premier League for Aston Villa in 38 appearances, Diaby has already scored half of that total in his first four games for Al Ittihad.
The Frenchman was in top form against Inter, registering the most shots (three) and shots on target (two), with his expected goals (xG) total of 0.24 only bettered by Benzema (0.55).
Trossard, 28, is in his fourth season with the Seagulls, and after never scoring more than eight Premier League goals in each of his previous three campaigns, he is on pace to set a new personal-best with seven in his first 16 appearances.
His exploits this season have included a hat-trick in a 3-3 draw against Liverpool, as well as goals against Manchester City and Chelsea, but he recently butted heads with head coach Roberto De Zerbi and has been left out of Brighton's last two matchday squads.
The Belgium international with 24 senior caps has also had his agent announce his intention to leave the club this month, triggering plenty of interest from fellow Premier League sides.
TOP STORY – CHELSEA WANT TROSSARD TO RECREATE MAGIC WITH POTTER
According to The Mirror, Chelsea are understood to now be a main player along with Tottenham and also Arsenal as the three clubs compete for Trossard's services.
Trossard had only six months remaining on his contract on the south coast, before Brighton reportedly activated a 12-month extension to ensure he would not be able to leave the club on a free transfer.
It is believed Chelsea have the most spending power of the trio, even after their £88.5million purchase of Shakhtar Donetsk winger Mykhaylo Mudryk, and Trossard remains a favourite of his former boss Graham Potter.
His asking price has been set at £25m, while the report adds any potential deal for fellow Brighton talent 21-year-old Moises Caicedo – also of interest to Chelsea as well as Liverpool – would cost "more than double" that £25m figure.
ROUND-UP
– The Mirror is reporting West Ham would like to bring in 29-year-old Manchester United centre-back Harry Maguire on loan.
– According to Sky Sports, Arsenalhave enquired about 23-year-old Bayer Leverkusen winger Moussa Diaby, but have been told he will not be available this month and will cost €100m (£88.5m) at the end of the season.
– Barcelonaare hoping to secure 32-year-old Manchester City midfielder Ilkay Gundogan on a free transfer at the end of the season, per the Telegraph.
– Fichajes is reporting Arsenalwill attempt to sign Chelsea's Raheem Sterlingafter failing to land the 28-year-old England international prior to his move to Stamford Bridge last year.
– According to The Independent, Real Madrid and Juventusare monitoring United 18-year-old Alejandro Garnacho after he rejected the club's most recent contract extension.
