The goal was Gillead's first at senior level and also capped off a superb performance from the youngster, who was later named man of the match.
Gillead's impact was even appreciated by Exeter's away support, as they applauded him off the pitch at the final whistle.
The Toon starlet tweeted:
What a win! What a team performance! Buzzing to have scored my first senior goal and get the win! Fans were unreal! Thanks for the messages!— Alex Gilliead (@AlexGilliead) October 17, 2015
Carlisle later confirmed:
Carlisle United FC (@officialcufc) October 17, 2015