The hosts grabbed a lifeline through Keiffer Moore's goal, but the promotion contenders were good value for their win.
Yeovil enjoyed a bright start without really troubling Tom Heaton in the visitors' goal, but fell behind in the 19th minute to an unstoppable strike from Ings.
The ball broke to him 20 yards out and he striker fired past Marek Stech.
The opener sparked Burnley into life and Ings continued to find pockets of space, showing why he has been linked with a move to the Premier League.
The former Bournemouth man gave the Glovers a scare when he found space in the area and hooked the ball into the home terrace.
For the Somerset side it was was a first-half performance that was indicative of their season - comfortable in possession, but toothless up front.
The first real chance of the second half arrived just five minutes in when Keith Treacy's curled free-kick was turned round a post by Yeovil's Czech goalkeeper Stech.
Burnley responded immediately when Vokes got ahead of his marker, but he turned his effort against a post.
The difference between the two sides was highlighted after an hour.
The hosts carved out the perfect opportunity to equalise when Luke Ayling's cross found Grant, whose header came back off the crossbar.
At the other end, Shane Duffy lingered on the ball, allowing Dean Marney to nip in and selflessly tee up Vokes for a tap in.
But Yeovil halved the deficit from an unlikely source on 79 minutes.
Moore was playing non-league football last season, but buoyed by his first professional goal in the FA Cup versus Leyton Orient, the substitute surged down the left wing and saw his cross-shot fly into the far corner.
Yeovil poured forward in search of a late equaliser - sending keeper Stech up for set-pieces - but Burnley held firm.
- Sports & Recreation
- Sam Vokes
- Danny Ings