MILAN - Adriano headed in the winner as the Nerazzurri saw off Anorthosis Famagusta in Matchday 3.
The Brazilian striker, Inter's all time top scorer in the Champions League, took his tally to 18 with a well taken goal just before the break.
The result sees Mourinho's men open up a three-point gap at the top of Group B, with Panathinaikos drawing 2-2 at home to Werder Bremen in tonight's other match.
Anorthosis had the first shot on target with Francesco Toldo, in for Julio Cesar, making a punched clearance from Dellas' well struck free kick.
From then on in it was all Inter, and Stankovic tried a repeat of his goal against Roma at the weekend, scything just over from 25 yards.
Muntari had a shot saved by Beqaj's foot after a brilliant move involving Brazilian trio Adriano, Maicon and Mancini as Inter pinned back the Cypriots.
Front men Adriano and Ibrahimovic then had two chances each before the Emperor rose unmarked in the box to head home a cross from Maicon, who turned Savio in the box after Ibrahimovic's crossfield pass.
Anorthosis saw more of the ball after the restart and went close to an equaliser through Katsavakis in the opening minutes. But the Nerazzurri stayed in control and created chances to build on their lead, with Muntari heading over a Mancini cross and Ibrahimovic slotting wide of the far post before substitute Julio Cruz drilled inches wide in the final stages.
Inter 1-0 Anorthosis Famagusta (HT: 1-0)
Scorer: Adriano 44.
Inter: 1 Toldo; 13 Maicon, 2 Cordoba, 26 Chivu, 4 Zanetti; 5 Stankovic, 19 Cambiasso (16 Burdisso 83), 20 Muntari; 10 Adriano (9 Cruz 82), 8 Ibrahimovic, 33 Mancini (77 Quaresma 63).
Subs not used: 12 Julio Cesar, 23 Materazzi, 39 Santon, 45 Balotelli.
Coach: José Mourinho.
Anorthosis Famagusta: 1 Beqaj; 22 Ocokoljic; 4 Katsavakis, 24 Constantinou, 12 Leiwakabessy; 6 Dobrasinovic (11 Frousos 88), 33 Dellas; 27 Bardon (16 Tsitaishvili 76), 17 Savio, 20 Laban; 9 Sosin (19 Taher 46).
Subs not used: 30 Nagy, 21 Panagi, 23 Samaras, 67 Theodotou.
Coach: Temuri Ketsbaia.
Referee: Howard Webb (England).
Booked: Katsavakis 62.