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In the first half, the Devon side did not pose much of a threat to Ilminster's goal.
The Blues, however, had a few close shaves, with efforts from Ed Butcher and Josh Phillips nearly finding the back of the net.
The game continued in a similar fashion after the break.
Exeter's central defenders were commendable, but Ilminster's Neil Martin and Harry Manley were equally impressive.
Manager Jason Behan introduced some substitutes, including Pablo Borges, who has scored 11 goals in seven games.
The fresh legs gave Ilminster some added impetus, and it was Borges who broke the deadlock in the 71st minute, heading home from a Butcher corner.
Borges was also instrumental in the second goal, scored during added time.
He held up the ball with his back to the goal, before passing it back to the advancing Josh Phillips.
Phillips then played a clever one-two with Marky Jones before confidently finding the bottom corner.
This marks Ilminster's second win in a week against the University side, with the students playing some good football but lacking the cutting edge up front.
Ilminster, who are second in the South West Peninsula League East Division, will face Bridport in the second-round cup tie.
The team consisted of Shay Allen, Manley, Lee Sweet, Drew Stride, player of the match Martin, Jones, Thomas Lee, Harvey Saunders, Butcher, Jordy Lovibond, and Phillips.
Substitutes Owen Burn, Caleb Pack, Jack Steer, and Borges all featured.
Ilminster will return to League action in the SWPL on Saturday, October 24, travelling to Newton Abbot Spurs for a 3pm kick-off.