Homer kicked all 10 of his attempts on goal - including two penalties from inside his own half - to add to two breakaway tries from Jonathan Joseph, a first-half touchdown from Topsy Ojo and a penalty try.
Jimmy Gopperth was Newcastle's top scorer with five penalties and two conversions, while Jamie Hueller and Darren Fearn grabbed the visitors' two tries in the second-half.
After an opening period littered with penalties, Irish took a 19-12 lead into the interval and they soon extended their advantage thanks to a couple of three-pointers from Homer and Joseph's try.
A penalty try in front of the posts put Exiles 39-15 ahead and despite Falcons' touching down twice in the latter stages, the hosts emerged as comfortable winners in their first game at the Madejski Stadium this season.
The victory is the second in a row for Toby Booth's men ahead of a trip to Gloucester next Saturday (1pm ko).
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