Fredy Guarin proved every inch the catalyst after playing a part in all three of his side's goals against the Azeri newcomers, who were no match for the Italians
Goals from Philippe Coutinho, Joel Obi and Marko Livaja fired the Nerazzurri to a comfortable three points on their travels despite Nicolas Canales' second-half reply, but the scoreline did not do the dominance exhibited by the visitors enough justice.
From the first whistle, Andrea Stramaccioni's young side were in control of proceedings, and were happy to adopt a patient build-up style. Nevertheless, Fredy Guarin's quick burst of pace saw him break the offside trap and allow Coutinho to flick home.
However, they suffered two momentary lapses in concentration. Firstly, Esteban Cambiasso sold goalkeeper Samir Handanovic short with a backpass, while soon after, on 23 minutes, Flavinho came a whisker away from touching a bent free-kick into the back of the net.
Yet the Colombian was at it again, racing towards the Neftchi box, and his drilled cross was aptly finished by Obi. The strike marked Inter's 500th in Europe, and the midfielder's spectacular celebration seemed appropriate enough, given the occasion.
And with just three minutes of the first-half remaining, Guarin capped off a fine period of play, using his vision to thread through a defence-splitting pass for Livaja to head home.
The hosts appeared down and out but they returned to the pitch with renewed vigour after the interval. Mahir Shukurov charged into the Inter box and forced Handanovic into a stop, before Julius Wobar took on Matias Silvestre and saw his low cross fall into the path of Canales at the far post, who finished with ease.
But unfortunately for Neftchi, they failed to build on that strike as the match faded into a scrappy affair. For Inter, they move level with Rubin Kazan at the top of their group, but the home side fall to the bottom of the table.