The Clarets made it into the last 32 of the Carling Cup, but once again had to work overtime to get past League Two opponents on another night of drama at Turf Moor.
A goal from substitute Chris McCann in the 105th-minute finally killed off Barnet, who showed that their first-round upset of Portsmouth was no flash in the pan.
For the second round running the Clarets saw a two-goal lead wiped out as the Londoners followed the lead of Burton Albion by forcing an injury-time equaliser to make it 2-2 and force extra time.
Goals from Jay Rodriguez - his fifth in two Carling Cup games - and Wade Elliott looked to have secured a more straightforward passage into round three.
But substitutes Steve Kabba and Ricky Holmes made sure the Bees would not be swatted away easily as they pushed Eddie Howe's men all the way, before McCann's first goal at Turf Moor since February, 2009 arrived in the nick of time.
As against Burton in the previous round, the Clarets took their time to get going on what turned out to be another long night.
Jay Rodriguez heads Burnley in front
And having failed to find an early goal, they must have been relieved not to have fallen behind before Rodriguez broke the deadlock.
The first 25 minutes had belonged almost exclusively to Burnley but they failed to take advantage of dominating possession as Charlie Austin headed wide from a Ross Wallace cross, Rodriguez saw a shot parried by Dean Brill and Ben Mee nodded a corner from the dangerous Keith Treacy past the post.
Wallace then missed the best chance of the lot as he dragged a shot wide after being sent clear by Rodriguez's sublime pass.
But if that was a wasted opportunity then Jason Price's miss moments later bordered on the criminal.
The veteran striker managed to mis-kick from inside the six-yard box with just Lee Grant, who did well to keep his eyeon the ball, to beat and must have been horrified to see the assistant referee keep his flag down when he looked to be standing yards offside.
However, that opening gave the underdogs an injection of confidence and with half an hour gone big defender Clovis Kamdjo powered a header wide from Mark Marshall's free-kick as they sensed the possibility of another upset.
Wade Elliott makes it 2-0 and celebrates
Marshall was proving a real handful and when he caused further problems in the Burnley box, Price got in a header which Grant grabbed on the line.
The Clarets countered with a Wallace effort which skidded just wide after the winger had been played in by Dean Marney.
And just when it looked as though they might be heading into the break goalless, Rodriguez pounced to further enhance his record in the competition.
Trippier provided the ammunition with a deflected cross from the right and while Rodriguez's header took a touch off Kamdjo, he was rightly able to add another goal to his Carling Cup collection with 39 minutes gone.
The Clarets were forced into a change of personnel when acting skipper Michael Duff picked up a knock to be replaced by David Edgar. And five minutes into the second half it was Edgar who almost got the second goal which might have been expected to have put the tie to bed.
However, the defender has never scored for the Clarets and he maintained that record when he poked a shot just wide after a Trippier free-kick had dropped invitingly into his path.
Chris McCann steers home the winner
Austin then went close to his fourth goal in as many games at Turf Moor this season with a fierce drive which flew just over the top but Barnet remained a threat on the break and could have been level with an hour gone.
Izale McLeod was beginning to make his presence felt and from his run and cross Sam Deering was presented with a chance which he directed inches too high when he looked a certain scorer.
Burnley needed the insurance of a further goal and when it finally came with 63 minutes gone it was a little gem.
Trippier's ball forward was cleverly helped into the path of Elliott by Austin's neat flick and Elliott - back in the side in place of the rested McCann - needed no second invitation to side-step the final defender and coolly beat Brill with a clam finish.
That should have been that, but Burnley's struggle to keep a clean sheet cost them again as Kabba pounced to make it 2-1 and launch the Bees' brave fightback.
The striker is just back from injury, but has forged a habit of scoring against the Clarets down the years and did it again when he arrived perfectly to steer in a low cross from Marshall.
Round three beckons
And after Rodriguez had failed to convert a Brian Easton cross at the other end, Kabba almost grabbed an equaliser with his low shot forcing Grant to plunge to his right to make a tidy save.
Having been taken to extra time by Burton, the Clarets didn't want a repeat but despite a late flurry of chances they couldn't find a third goal to make sure of an early finish.
Treacy, who was a real livewire all night, forced Brill to tip his low shot around the post and from the resulting corner substitute Zavon Hines saw his shot blocked on the line.
Hines then raced onto a Treacy pass but was defeated by the angle as Brill denied him his first Burnley goal and in the third minute of stoppage time lightning did strike for a second time as Barnet forced the extra half-hour.
Grant looked to have dashed their hopes with a fine save from Marshall's free-kick but Holmes reacted quickest to reach the rebound to ram home the most dramatic of equalisers.
Lee Grant makes a fine save, but the rebound forces extra time
Unlike the previous round Burnley could not respond with a rapid counter thrust but as the prospect of penalties began to loom they went back in front in the final minute of the first half.
McCann had replaced Treacy moments before the end of normal time and the captain was in the right place at the right time to benefit from a bout of pin-ball in the penalty area, following another Easton cross, to guide home his first goal of the season and finally see his side through.
Burnley: Grant, Trippier, Easton, Duff (Edgar 45), Mee, Marney, Elliott, Treacy (McCann 89), Rodriguez, Austin (Hines 70), Wallace. Subs: Hewitt, MacDonald, Amougou, Jensen.
Booked: Rodriguez 76
Barnet: Brill, Senda, Uddin (Geohaghon 89), Kamdjo, Parkes, Hughes, Marshall, Deering (Holmes 77), Byrne, Price (Kabba 67), McLeod. Subs: O'Brien, Cox, Vilhete, Taylor.
Booked: Parkes 70, 98
Referee: Chris Sarginson