Inzaghi was promoted from his role as youth-team coach ahead of the new season after the departure of Clarence Seedorf, who was sacked following a disappointing 2013-14 campaign, in which Milan finished eighth.
The club legend has since added the likes of defender Alex and goalkeeper Michael Agazzi to his squad, and the former was handed a first start in the red-and-black shirt on Wednesday.
However, it was Stephan El Shaarawy who put Milan ahead against their fourth-tier opposition in the 24th minute when he latched onto the end of a Cristian Zaccardo cross from the right, tapping home the rebound after initially hitting the post.
El Shaarawy was restricted to six top-flight appearances by a persistent foot problem last term, and his goalscoring start to the 2014-15 season will be hugely encouraging for Inzaghi.
It was another Zaccardo delivery that unlocked the Renate defence again 10 minutes into the second half, with Riccardo Saponara on hand to apply the finish this time around.
Inzaghi had made six changes at the break and continued to tinker with his XI as the second period progressed, but both goalkeepers stayed untroubled for the remainder.
