Last season's runners-up Roma advanced to their fourth European semi-final in a row.
Noah Okafor salvaged a hard-fought point for Milan in the 84th minute on a hot spring day in Reggio Emilia, but second-placed Milan still risk conceding the Scudetto to Inter in a hotly-anticipated derby despite coming back from two goals down.
AC Milan strolled past 10-man Lecce 3-0 on Saturday to consolidate second place in Serie A and take another step towards Champions League qualification.
AC Milan's owners said on Thursday they will build a 70,000-capacity new stadium for the seven-time European champions that will serve as a multi-purpose venue.
Marcus Thuram was key to Inter's win at a soaking Stadio Olimpico in Rome as, with his team trailing at half-time, the France attacker made it two goals each shortly after the break and forced the Angelino own goal which put Inter ahead in the 56th minute.
The fixture was stopped in the 16th minute in honour of Maignan's shirt number while a famous King quote was displayed on the San Siro's big screens.
Udinese will ban for life a man found to have racially abused France goalkeeper Mike Maignan, the Serie A club announced on Monday.
"I said we cannot play football like this," Maignan said
The 37-year-old Giroud was in the perfect position to head in their second goal before his brilliant back-heel flick set up Theo Hernandez for the third.
AC Milan consolidated their place in Serie A's Champions League positions on Sunday with a straightforward 3-0 win over lowly Empoli.
Atalanta beat Sassuolo 3-1 on Wednesday to qualify for the Italian Cup quarter-finals where they will meet AC Milan.
AC Milan starlet Francesco Camarda made history on Saturday after becoming the youngest ever player to play in Serie A during Saturday's 1-0 win over Fiorentina.
Mazzarri's team are still seven points behind leaders Inter Milan who travel to Turin on Sunday for the weekend's big match at second-placed Juventus
Gianluigi Donnarumma will be given a fierce reception on Tuesday when he faces crisis-club AC Milan at the San Siro for the first time since jumping ship for Paris Saint-Germain and becoming public enemy number one.
AC Milan are in a difficult group that includes Borussia Dortmund and Newcastle United.
Paris Saint-Germain's Champions League clash with AC Milan this week will see the French club come up against one of the many outstanding talents they have let slip away in recent years.
Khvicha Kvaratskhelia helped put Napoli's Serie A title defence back on track with a brace in Saturday's 3-1 win at Verona which moved the champions four points behind leaders AC Milan.
Inter rebounded from their first loss of the season midweek against Sassuolo thanks to a sensational second-half display from Martinez.
Portugal winger Leao netted his third goal in as many league matches in the eighth minute at a sodden San Siro to move Milan up to second on 12 points from five games