The Chiefs ran in six tries at Kingston Park to make it successive wins since the competition resumed after the Six Nations
Exeter wings Paul Brown-Bampoe and Campbell Ridl scored two tries apiece, with Olly Woodburn and Stephen Varney also crossing for the visitors
The five points lifted Exeter above Leicester ahead of the bulk of the weekend's matches.
It also meant the Chiefs opened up an eight-point lead over fifth-placed Bristol as Exeter chase a top-four finish that would secure a play-off place for the first time since 2021.
Defeat was Newcastle's 11th loss in 12 league games this season, with the Red Bull-backed team still four points adrift of Harlequins.
All Newcastle had to show for their efforts was a brilliant solo try from Christian Wade and a late score from Connor Hancock.
But with relegation being scrapped as part of a major shake-up, Newcastle can still look forward to remaining in the top flight.