Tom Nichols and David Wheeler had put the hosts two goals ahead before the break but they needed Hoskins’ effort to claim all three points after the Glovers had fought back.
Following a scrappy first half hour, where the highlight was the touching minute’s applause in both the seventh and ninth minutes for former Yeovil and Exeter striker Adam Stansfield, the home side got the breakthrough after 31 minutes.
Connor Roberts, who only signed for Yeovil on Friday night, held back Alex Nicholls inside the box and Nichols made no mistake from the spot, sending Chris Weale the wrong way from 12 yards.
The goal visibly lifted Exeter and the Grecians made it 2-0 four minutes before half-time when Wheeler latched onto David Noble’s perfectly weighted pass and slipped the ball past Weale.
Yeovil needed a response after the break and they got it immediately as substitute Harry Cornick appeared to get the final contribution with his first touch just after the hour.
The young winger was then fouled inside the box by Christian Ribeiro, which allowed Matt Dolan to level the scores from the spot.
But Wheeler hit the post for Exeter before Hoskins latched onto Matt Oakley’s pass and knocked it past Weale and into the net with six minutes remaining.