Byron Webster nodded the visitors in front on the stroke of half-time before second-half efforts from Miller and Joe Edwards finished the job for the Sky Bet Championship strugglers.
Glovers manager Gary Johnson made four changes to the side which had slumped to a 2-1 defeat to Doncaster last time out, with Miller, Liam Davis, Adam Morgan and John Lundstram coming into the side in place of Joe Ralls, Sam Hoskins, Fraser Fyvie and the injured Jamie McAllister.
The hosts enjoyed the lion's share of possession in the early stages and came close to taking the lead in the 24th minute, but Marco Cassetti's strike was blocked by Liam Davis.
The Hornets carried on pushing, but the visitors resisted and it was Johnson's men who broke the deadlock in first-half stoppage time.
Webster got on the end of Davis' corner to nod the ball past Hornets goalkeeper Jonathan Bond at the back post.
Yeovil soaked up early Watford pressure in the second half before doubling their advantage eight minutes after the break.
Edwards flew down the wing before delivering a precise ball towards the head of Miller, who buried his finish in the back of Bond's net.
The away side continued to defend resolutely and to frustrate Watford, who came closest to pulling one back when Diego Fabbrini let fly from range, but his effort was blocked by Edwards.
Yeovil improved as the second half went on and added to their lead in the third minute of stoppage time when Edwards steered the ball past Bond from the middle of the area after good build-up play from on-loan Everton midfielder Lundstram.