The duo struck either side of Graham Cummins’ leveller as Ronnie Moore’s men, who were 10 points adrift at the foot of the table in January, secured their Football League status.
The hosts took a 16th-minute lead when Fenwick took advantage of a slip from Jordan Moore-Taylor to race on to Hugill’s flick-on, before composing himself and coolly sliding the ball into the corner.
But Exeter equalised immediately, an unmarked Cummins heading home Liam Sercombe’s corner moments after being denied by Scott Flinders in identical fashion.
Hartlepool missed a glorious chance to retake the lead when James Hamon denied Fenwick, but a second came on the stroke of half-time.
Aaron Tshibola followed a surging run with a pin-point through-ball and Hugill powered home with his left foot.
Hartlepool continued to edge proceedings in the second period, almost grabbing a third when Fenwick’s strike was cleared off the line.
However, it mattered little as Pools grabbed the decisive points to end Exeter’s faint play-off hopes.