A miserable and pointless September left Wednesday in the Championship relegation zone and manager Dave Jones under pressure heading into this Turf Moor encounter, but the Owls showed remarkable resilience to claim their first point since August 25.
Charlie Austin's second hat-trick of the season was not enough for Burnley to secure the win as Chris O'Grady struck twice before Michail Antonio netted a late leveller.
Austin handed the Clarets the lead against the run of play in the 22nd minute only for O'Grady to level within 75 seconds.
When Austin struck once more before the break, Jones' half-time team-talk took on added importance and his men responded, O'Grady doubling his tally after going seven games without a goal.
And even after Austin completed his treble, taking his season's tally to 14 in 11 matches, Antonio was on hand to provide one final twist in a dramatic tale.
The game started at break-neck speed and both sides had chances to score inside the opening 15 minutes. Antonio fired over on the turn for the visitors, while Martin Paterson drilled a long-range shot narrowly wide for the hosts.
But just as Wednesday were beginning to assert themselves, Burnley took the lead. Kieran Trippier delivered from the right and Austin was there to head home.
A response was needed and came almost instantly. From the kick-off, Antonio advanced into the box and squared the cross for O'Grady, who made no mistake with his header from 12 yards.
There was little chance of any respite for either defence and Lee Grant had to dive full length to keep out Everton loanee Ross Barkley's powerful strike.
The young midfielder passed up an even more presentable chance moments later when he steered wide from just six yards out.
Wednesday were made to pay for their profligacy when Austin pounced once again.
Trippier was the provider and when Jermaine Johnson failed to clear, Austin was in prime position to make it 2-1.
The home side were in the ascendancy and could have put the game to bed before half-time, if only David Edgar and then Austin had been more measured when presented with excellent scoring opportunities inside the box.
Jones had the chance to reorganise and his charges at the break and, after surviving a spell of early second-half pressure, they hit back.
Jay Bothroyd laid on the pass for O'Grady and he finished calmly into the bottom corner with his left foot.
Antonio could have capped a fine comeback when the ball fell for him six yards out, but he snapped at his shot and Grant did well to tip it wide.
Austin left the Owls with that familiar sinking feeling when he rifled home from 20 yards with six minutes remaining, but Antonio outdid him with an even sweeter strike from 25 yards to ensure, perhaps fittingly, that it ended all square.