MILAN - Adriano scored an early goal and Zlatan Ibrahimovic added an outrageous second right after Taddei's equaliser as Inter knocked out the Tim Cup holders and progressed through to the last four.
After wins in the Italian Super Cup and the league, José Mourinho's Inter completed a hat-trick of victories over Roma to set up a two-legged semi-final against this coming Sunday's Serie A opponents Sampdoria, who ousted Udinese after a penalty shootout.
Mourinho made a string of changes to the side that lost at Atalanta at the weekend, handing 18-year-old Italian full-back Davide Santon his competitive debut and pairing Adriano in attack Ibrahimovic.
Roma had a goal ruled out early on when Mirko Vucinic saw the ball over the line with his hand.
Inter hit straight back and Adriano took advantage of a collision between Mexes and Juan before shrugging off a challenge from Riise and shooting low past Artur for his seventh goal in games against the Giallorossi.
Stankovic almost doubled Inter's lead with what would have been a candidate for goal of the season, striking the crossbar with a stunning volley on the turn from Maicon's cross.
Spectacular efforts were the order of the day and Ibrahimovic tried to lob Artur after ghosting into the box but the Giallorossi keeper produced a tipped save.
The rest of the half belonged to Roma. Perrotta tested Francesco Toldo with a well taken angled shot and the veteran keeper then denied Vucinic before keeping out Perrotta's deflected shot.
The Ibra-Adri partnership continued to work well after the restart and the Swede, voted Italy's Player of the Year for 2008 several days ago, had the crowd gasping with an incredible volley after a powerful move by his strike partner.
Set to make way for Pizarro, Taddei silenced the Meazza with a cracking rising drive from Perrotta's pull-back as Roma levelled in the 61st minute. But Inter provided the perfect reaction and were back in front within sixty seconds when Ibrahimovic spectactularly hooked home after Artur parried Samuel's header.
Toldo pulled off another expert save from Pizarro, and Aquilani, on for the last ten minutes, hit the sidenetting and sent wide an overhead kick as Roma fought hard to force extra time.
Inter 2-1 Roma (HT: 1-0)
Scorers: Adriano 10, Taddei 61, Ibrahimovic 62.
Inter: 1 Toldo; 13 Maicon, 16 Burdisso, 25 Samuel, 39 Santon; 4 Zanetti, 19 Cambiasso, 20 Muntari (33 Mancini 86); 5 Stankovic; 8 Ibrahimovic, 10 Adriano (26 Chivu 77).
Subs not used: 12 Julio Cesar, 7 Figo, 24 Rivas, 45 Balotelli, 77 Quaresma.
Coach: José Mourinho.
Roma: 25 Artur; 3 Cicinho, 5 Mexes, 4 Juan, 17 Riise (24 Menez 71); 11 Taddei (8 Aquilani 79), 16 De Rossi, 20 Perrotta, 33 Brighi; 19 Baptista; 9 Vucinic (7 Pizarro 60).
Subs not used: 27 Julio Sergio, 15 Loria, 26 Greco, 77 Cassetti.
Coach: Luciano Spalletti.
Referee: Daniele Orsato (Schio).
Booked: Juan 8, Vucinic 10, Samuel 23, Perrotta 45+1, Mexes 83.