Dean Marney made his return and Rouwen Hennings opened his account for the club as the Clarets fought back from two goals down to salvage a point against Cardiff City.
The game seemed lost with five minutes remaining as Sean Dyche's side battled a two-goal deficit in South Wales, but a late strike from Hennings coupled with an own goal from Connolly saw the game finish 2-2.
On an uncompromising playing surface, married with an unrelenting deluge in South Wales, the Clarets were slow to acclimatise to the conditions.
Scott Malone sliced an early volley wide from inside the penalty area after Kenwyne Jones's accidental flick from Tendayi Darikwa's attempted clearance fell fortuitously in to his path.
And that set the tone, for the first half-an-hour of the fixture at least. Tom Heaton plunged to his post to prevent Jones's header from creeping in to the corner moments later after the Trinidad and Tobago striker out-jumped his marker to meet Peter Whittingham's cross.
The Bluebirds kept up the pressure, proving threatening in the air, and a combination of centre-backs Matthew Connolly and Sean Morrison almost proved clinical but the latter's header from close range was flicked over the bar by Heaton.
A moment of respite for the visitors saw Michael Keane, with three goals to his name so far this term, flick wide of the target from David Jones's corner after Joey Barton's attempt from the edge of the box was deflected wide.
But City came again and this time it was Tony Watt who proved troublesome as he carved through Burnley's midfield and drove at their backline before cutting a right-footed strike across Heaton and narrowly wide of the upright.
After Joe Ralls flashed an ambitious effort high and wide from Whittingham's quickly taken corner, Heaton was forced to scramble to his line to turn Craig Noone's attempt over the top after the ball had looped off the boot of Keane.
Eventually, however, Sean Dyche's side got a foothold in the game and created two of the best openings of the half.
Championship leading scorer Andre Gray created the opportunity when beating David Marshall to a through ball and, with the goalkeeper out of position, the striker picked out George Boyd whose first time effort was blocked on the line by Connolly.
The pair combined again soon after when Gray beat Malone down the right hand side and found Boyd once more but, somehow, the winger fired over.
In the immediate aftermath, in unison with boss Sean Dyche, who demonstrated animatedly from the sidelines, Boyd led appeals for a penalty with claims that his attempt had been handled.
And the away side were made to pay for that spell of profligacy in the 41st minute when Aron Gunnarsson gave Cardiff City the lead.
The Icelandic midfielder leapt to meet Ralls's delivery from a set-piece and his header flicked up off the slippery pitch to beat the outstretched arm of Heaton and find the corner.
After the interval it was the home side who continued to take command. Gunnarsson attempted to beat Heaton for a second time when firing from the edge of the penalty area, but this time the England international was equal to the strike. Then Jones lofted a header just over the bar from Whittingham's corner.
Cardiff City's second of the afternoon arrived in the 64th minute and, again, it all looked too easy for the hosts.
City substitute Joe Mason, who had replaced Watt just minutes earlier, drew a fine save from Heaton when latching on to Mason's incisive pass but from Whittingham's resulting corner, which he sat up dangerously in the six-yard box, Morrison nodded home to double the advantage.
That prompted the change as Marney was introduced at the expense of Jones in the 67th minute.
The 31-year-old midfielder, who signed a new two-year deal at Turf Moor in September, made his comeback after being sidelined through injury for nine-and-a-half months.
Marney, who suffered a cruciate knee ligament injury in February where he was withdrawn at half-time in the 2-2 draw with West Brom in the Premier League, proved the inspiration to the away side's fight back.
Matthew Taylor, who had replaced Chris Long, went close for the Clarets with a trademark free-kick from distance, but Marshall did well to palm to safety after the ball skidded off the wet surface.
With five minutes of normal time remaining, Hennings gave the Clarets hope when turning well to convert Boyd's centre.
Rejuvenated, the visitors pressed for the leveller and their perseverance was rewarded deep in to stoppage time.
Keane's header from Marney's delivery caused confusion inside City's penalty area before the ball hit the shins of Connolly before resting in the net, sparking delirium among the travelling support.
The Clarets now go in to the derby with Preston North End next Saturday on the back of an eight-game unbeaten run.