Lukaku is enjoying an excellent first season with the Nerazzurri following his move from Manchester United and went into Tuesday's clash at San Siro with 16 goals in 24 games in all competitions.
He added to that tally with a goal in each half against a Cagliari side an impressive sixth in Serie A despite a poor run of form, needing only 21 seconds to open the scoring after Christian Oliva inadvertently played him through on goal.
His goals were sandwiched by a tap-in from Borja Valero and Antonio Conte's Serie A challengers were rarely threatened until Oliva atoned for his earlier error with an emphatically taken consolation.
Andrea Ranocchia restored Inter's three-goal lead late on and they will now switch focus back to an engrossing title battle with Juventus.
Lukaku was ruthless in punishing Oliva's error as he calmly slotted into the bottom-right corner and he would have had a second if not for a questionable offside decision, the Belgium striker adjudged to have strayed as he turned home a near-post cross in the 11th minute.
The former United man was unable to connect with Nicolo Barella's right-wing cross, but it mattered not as the delivery was bundled in by Valero at the second attempt.
Cagliari continued to afford Lukaku opportunities and four minutes into the second half he steered a difficult header into the net from another superb Barella ball into the box.
Radja Nainggolan, on loan at Cagliari from Inter, struck the post with a vicious drive, before Oliva beat Samir Handanovic with a rasping finish from Alberto Cerri's backheel lay-off.
However, poor marking at a corner allowed Ranocchia to make absolutely sure of victory as he converted from substitute Cristiano Biraghi's set-piece 10 minutes from time.