YEOVIL ran into double trouble as substitutes Keith Treacy and Scott Arfield helped to maintain the Clarets unbeaten start to the season.
The Clarets found the newly-promoted Glovers a tough nut to crack until Sean Dyche turned to the bench midway through the second half.
Treacy immediately came up trumps with a fortuitous, wind-assisted cross that put the Clarets in front with time running out.
And Arfield had more than a helping hand in the second three minutes later when his shot cannoned in off striker Sam Vokes.
The result was tough on Yeovil, who more than played their part in a game that for long periods threatened to remain goalless.
But that won’t matter to Dyche and the Clarets, who climbed to third in the Championship table following a scintillating start to the season.
Sean Dyche named an unchanged line-up for the fourth successive game for this historic meeting between the two sides.
Opposite number Gary Johnson made changes to his first 11, with on-loan goalkeeper Sam Johnstone joining the club at the 11th hour following an injury to Marek Czech.
And the youngster was tested as early as the fifth minute when Ross Wallace let fly with a typical long-range effort that the sprawling keeper turned round the post.
Sam Vokes then volleyed over on the turn as the Clarets overcame a wobbly start to get back on the front foot.
And after James Hayter had flashed a shot wide, Vokes had the best chance of the game following a surging run by Dean Marney.
The midfielder sent Vokes clear on the left of the area, but his chip over an advancing Johnstone was just wide of a gaping goal.
However, Yeovil wasted an even better opportunity to grab the lead 10 minutes before half time with a contender for miss of the season.
Paddy Madden’s angled drive was parried by Heaton and Liam Davis, unmarked four yards out, could only prod his first time effort over an open goal.
And in a half of spurned chances, it was Vokes again who ended the half by heading over from six yards after being picked out by Trippier’s peach of a cross.
The second half bean in similar vein, with Yeovil again impressing on the break and Burnley struggling to build up a head of steam.
A curling Stanislas effort wide of the far post just before the hour mark was the best the hosts could muster against resolute opponents.
Yeovil defender Daniel Seaborne came closest for the visitors when he planted a header wide of the post midway through a half that was becoming tougher by the minute due to driving rain and a swirling wind.
With just over 20 minutes remaining, Dyche mad a double change by replacing Stanislas and Ross Wallace with Scott Arfield and Treacy.
And the winger had the luck of the Irish with 16 minutes remaining as his curling left wing cross bent wickedly in the wind and sailed in at the near post with Johnstone desperately trying to keep it out at his near post.
Seconds later, the other substitute almost had his moment as, from Danny Lafferty’s pass, Danny Ings sent Arfield clear.
But after a couple of touches to compose himself the Scot dragged his shot across goal and wide of the far post.
However, the crucial second was not long in arriving. David Jones swing over a right wing cross that Ings headed against the post as he came close to scoring in the eighth successive game.
But the punishment for Town was the same as Arfield’s follow-up shot blasted off the back of Vokes and into the centre of goal.
Jones forced Johnstone to tip over a curling free kick and Vokes saw his firm downward header saved as the Clarets suddenly turned up the heat.
And there was almost a third for Burnley and a brace for Vokes after Treacy teed-him up minutes from time, only for Luke Ayling to clear off the line.
Burnley: Heaton, Lafferty, Long, Shackell, Trippier, Wallace (Arfield 68), Jones, Marney, Stanislas (Treacy 68), Ings (Noble 90), Vokes
Subs: Cisak, Mee, Edgar, Stock
Booked: Marney 48, Wallace 51
Yeovil: Johnstone, Ayling, Edwards, Tate (Ngoo 65), Webster, Seaborne, Dawson (Ralls 82), Upson, Hayter (Hoskins 65), Davis, Madden
Subs: Dunn, McAllister, Grant, Foley
Booked: Davis 76, Webster 80
Ref: Scott Duncan
Att: 10,085 (363)