A trademark Austin header in the 82nd minute gave new manager Sean Dyche his second victory in the space of four perfect days.
And in doing so, the 23-year-old became the fastest player in Burnley history to reach 20 goals as he notched for the sixth home game running.
But if Austin was the match winner, he would be quick to share the praise with his team-mates who again showed a collective desire to become only the second team in 11 games to beat a Leeds side who have become the division’s draw specialists.
And a back four which has been much maligned for large parts of the season - along with goalkeeper Lee Grant - deserved equal status as they ensured a third successive home clean sheet at Turf Moor, which is again becoming the base for a surge up the table.
After winning his opening game, Dyche understandably kept changes to a minimum with the return of the fit-again Chris McCann in place of David Edgar the only difference to his team sheet as the Clarets looked to end a five-game losing streak against their Roses rivals.
And much else stayed the same as Burnley picked up where they left off against Wolves at the weekend with a positive start which allowed the visitors no time to settle.
The Clarets pressed all over the pitch to keep winning possession and with Dean Marney and Chris McCann constantly breaking forward from midfield it was largely a claret and blue dominated first half.
Marney got himself into some outstanding positions and he almost marked his 100th-appearance for the Clarets with a goal after seven minutes.
Ross Wallace continued his recent impressive form with a fierce drive which Paddy Kenny could only parry and when Marney pounced, it took a smarter save from the Leeds keeper to block from close range.
Leeds barely mustered a threat, although the two occasions they did cause concern in the Burnley ranks came courtesy of former Blackburn forward El Hadji Diouf.
The Senegalese dragged a shot wide via a deflection and then as Burnley began to really crank up the pressure put a better chance just over the top as United mounted a rare counter-attack.
That was only a brief respite, though, as Dyche’s men forced the pace further, the lively Martin Paterson testing Kenny from long range after half an hour before Marney fired into the side netting after being found by Brian Stock.
And twice just before the break the Clarets almost broke the deadlock. Only a fine save from Kenny kept out Trippier’s thundering drive before Charlie Austin saw his effort from the ensuing corner deflected just wide of the post as Leeds held out.
Kenny remained the busier keeper at the start of the second half as he saved from McCann and a Wallace free-kick.
But it was largely long-range stuff from the Clarets as they struggled to find the killer blow and with almost an hour gone the hosts were forced to make a change when the in-form Ben Mee limped off with a foot injury to be replaced by Danny Lafferty.
With the Clarets unable to make their territorial advantage count, Leeds grew in confidence and with 62 minutes gone created arguably the best chance so far.
Again Diouf was heavily involved and when he laid the ball off for Aidan White, the little midfielder should have made Grant work harder with a finish that the Clarets’ keeper was able to help around the post.
Under sustained pressure for the first time the Clarets showed the resolve that has epitomised their recent home performances to keep United at arm’s length.
And with 15 minutes to go they almost got their noses in front. McCann’s driving run from midfield had Leeds on the retreat but from his pass Austin only had time to stab the ball goalwards and his effort went too close to Kenny to extend his scoring streak.
Austin then headed at Kenny from a Marney cross as Burnley, helped by the added presence of Sam Vokes in attack, gathered themselves for a late push.
And with eight minutes of regulation time left it paid off with a magnificent goal to win the day.
Starting with Wallace's ball inside on half way, McCann then delivered a sublime pass inside replacement full-back Danny Pugh for Trippier to deliver the kind of cross strikers dream of.
And with Austin turning everything he touches into goals it was an opportunity he wasn’t about to pass up, soaring to power a downward header beyond Kenny to keep Burnley climbing.
With Turf Moor euphoric there was one chance left for Leeds to spoil the mood but Grant’s superb save from Jason Pearce in the dying moments ensured another clean sheet as Dyche’s dream start continued.
Burnley: Grant, Trippier, Mee (Lafferty 59), Duff, Shackell, Stock (Vokes 64), Marney, McCann, Wallace, Austin, Paterson. Subs: Ings, Edgar, Stanislas, Bartley, Jensen.
Booked: Marney 90
Leeds United: Kenny, Peltier, Drury (Pugh 81), Pearce, Byram, White (Kisnorbo 86), Brown, Tonge, Austin, Becchio (Varney 86), Diouf. Subs: Green, Norris, Gray, Ashdown.
Booked: Drury 69
Referee: Geoff Eltringham