There was little to separate the teams in a goalless first half, with Hapoel spurning a couple of glorious chances.
Vitor broke the deadlock after 54 minutes when Lúcio Maranhão was released down the inside-right channel and fired a low centre across goal that Vítor side-footed into the net at the far post.
And there were scenes of jubilation 15 minutes later when Israeli international Buzaglo capped a superb all-round performance by curling a free-kick over the wall and into the net.
Hapoel's next match in the competition comes at home to Southampton on September 29. The Saints lead Group K on goal difference after defeating Sparta Praha 3-0.
Elsewhere in the competition, Maccabi Tel Aviv threw away a 3-0 advantage to lose 4-3 against Zenit St Petersberg. Haris Medunjanin (2) and Vidar Orn Kjartansson registered for Maccabi who had Eli Dasa sent off.
INTER: Handanovic, Felipe Melo (sub: Icardi), Palacio (capt), Biabiany (sub: Candreva), Ranocchia, Medel, Eder, Murillo, D'Ambrosio, Nagatomo, Brozovic (sub: Banega 46)
HAPOEL: Goresh, Bitton, Vitor, Tzedek (capt), Nwakaeme, Buzaglo (sub: Sahar), Hoban, Taha, Lucio Maranhao, Ogu, Korhut (sub: Turjman 85)
GOALS: Vitor 54, Buzaglo 69