Andre Gray’s third minute equaliser from the penalty spot earned the Clarets a valuable point and extended their unbeaten run to eight games.
Gray scored his seventh Turf Moor goal in four outings in an explosive start to cancel out Bobby Zamora’s first minute opener.
And as a tight game wore on, the Clarets will feel they had the chances to finally end the Football League’s only remaining unbeaten record, with Scott Arfield twice coming agonisingly close.
German striker Rouwen Hennings replaced the injured Sam Vokes up front, with Dean Marney making the bench in a long awaited return from a knee injury.
And the game set off at a breakneck pace, with both sides on target in the opening three minutes.
It was the visitors who took a shock lead after exactly 60 seconds.
Tom Heaton’s wonderful fingertip save tipped Tomer Hemed’s strike onto the crossbar, but Zamora reacted quickest at the far post to put the Seagulls in front.
However, that lead lasted just two minutes as Simon Hooper pointed to the spot after Michael Keane was clearly manhandled in the box by Lewis Dunk from David Jones’ corner.
That allowed Gray to rifle in his 11th goal of the season, bring the Clarets level and put the striker on the brink of becoming the first ever Burnley player to score twice in four successive home games.
And the frenetic start didn’t stop there!
The Clarets were awarded a free-kick four minutes later, and George Boyd’s 25-yard driven effort was fumbled by David Stockdale, before being eventually cleared to spare the former Fulham goalkeeper’s blushes.
The game finally settled, before both sides tested their opposition goalkeeper midway through the first half.
Boyd’s perfect cross found Hennings six-yards out, but his stabbed effort was wonderfully clawed behind by Stockdale.
Bruno Slator’s out-swinging cross to the penalty spot was then met by Zamora, but his powerful header was comfortable for England squad member Heaton.
And the Clarets nearly completed the comeback before half time in an entertaining contest.
Boyd – again in the thick of the action – perfectly threaded-in Gray, but his diagonal strike was brilliantly blocked wide by Brighton captain Gordon Greer.
In comparison to the first half, the second got off to a somewhat sedate start, with Chris Houghton’s side coming closest 20 minutes in.
Hemed controlled at the edge of the box before going for goal and it took a vital block from the experienced Michael Duff to clear.
But as the game entered the latter stages it was the Clarets and Arfield who looked the most likely to break the second half deadlock.
First the Scot played a neat one-two with Boyd, before a rasping strike from the former Huddersfield Town midfielder whistled inches over the angle.
Gray’s persistence down the right flank then ended with a low cross aimed for strike partner Chris Long, but the delivery evaded everyone allowing Arfield a clear shot at goal, which he pulled agonisingly wide of the far post.
And when Long’s last minute effort wide from six-yards was deemed offside by the officials, it was clear that both sides would share the spoils.
Burnley: Heaton; Darikwa, Duff, Keane, Mee; Boyd, Jones, Barton, Arfield; Hennings (Long 61), Gray
Subs: Gilks, Ward, Kightly, Taylor, Lowton, Marney
Goals: Gray 3’
Yellow: Mee 72’
Brighton: Stockdale; Saltor, Greer, Dunk, Rosenior; March, Stephens Kayal, Murphy; Hemed (Manu 82), Zamora
Subs: Maenpaa, Goldson, Holla, Forster-Caskey, Chicksen, Akindayini
Goals: Zamora 2’
Yellow: March 53’, Greer 86’, Dunk 88’
Attendance: 15,622 (375 away)