The Belgium forward was involved in two goals – scored in each half by Lautaro Martínez and Hakan Çalhanoglu – and home fans applauded him enthusiastically when he made way for Edin Dzeko in the 68th minute on Saturday.
Dzeko set up fellow substitute Joaquin Correa for the third goal in the 82nd.
Lukaku crashed a header off the crossbar before the break as he almost added to his goal from Inter's opening win over newly promoted Lecce last weekend.
Inter dominated from the start but home fans had to wait till the 35th minute for Martínez to fire in the opener. Nicolo Barella sent in a cross that Lukaku headed back for the Argentine to unleash his shot inside the left post.
Lukaku was involved again in the 52nd when he skipped past one defender and was faced by five more players when he passed to Milan Skriniar. Skriniar's attempted return pass was blocked but fell kindly for Çalhanoglu to score.
Also Saturday, Domenico Berardi's brilliant first-half goal was enough for Sassuolo to defeat Lecce 1-0.
Udinese had Nehuen Perez sent off before the break but goalkeeper Marco Silvestri denied visiting Salernitana in a scoreless draw.
Lazio drew at Torino 0-0.