Clarke Carlisle's goal in added on time gave 10 man Burnley a draw after David Norris looked to have won it for Blues.
Norris, who kept the skipper's armband after scoring twice in midweek as Town beat Exeter in the Carling Cup, backheeled the ball into the net from three yards on 85 minutes after Jon Stead had headed a corner back across goal.
The Clarets salvaged a point though, Carlisle's flashing header from Graham Alexander's corner going in at the far post.
Stead had gone closest to breaking the deadlock for Blues before Norris' strike while it took a brilliant stop from Marton Fulop to deny Wade Elliott in the first-half.
Andros Townsend was handed his debut for Town after joining on a year's loan from Tottenham in midweek. Jon Stead kept his place in attack, with Luke Hyam recovering from a shin injury to line up in the middle of the park.
Shane O'Connor won a free-kick for Town inside the first five minutes, Burnley scrambling the ball clear from Grant Leadbitter's delivery, then Tamas Priskin firing over from the angle.
Martin Paterson had the same result when presented with a similar chance at the other end, Townsend then sending Brian Jensen scrambling across his line as chances were created at both ends.
Andre Bikey's diving header prevented Stead getting on the end of Townsend's cross before Marton Fulop came to Blues' rescue midway through the half, throwing himself to his left to make a terrific save from Wade Elliott after Ross Wallace's astute pass.
Paterson hooked the ball over the bar after Wallace's free-kick had fallen into his path 10 yards out, before Roy Keane's side had their best opening of the half, Townsend's delivery flashing across goal - Stead unable to convert at the far post.
Townsend tested Jensen from 20 yards as the loanee enjoyed a bright opening 45 minutes, the England U19 international willing to run at players and shoot on sight.
Edgar picked up the only yellow card of an entertaining first-half for a challenge on Leadbitter and the Town midfielder was caught with a challenge from Clarke Carlisle just before the break, which forced Blues into a change with Colin Healy the replacement for the second-half.
The Republic of Ireland international was immediately in the action, throwing himself at Stead's cross, the ball drifting wide of Jensen's net.
Fulop had to move quickly to tip over Dean Marney's cross, the former Tottenham and Hull midfielder volleying over from the corner.
Healy sent a free-kick over the bar after Carlisle brought down Priskin, the Hungary international then failing to get his shot on target eight yards out, Stead's cross hacked clear by Edgar as Town looked the more likely to open the scoring.
Burnley made a first change on 67 minutes with Paterson making way for Chris Eagles, Blues following with a swap five minutes later with Townsend replaced by Ronan Murray for his League debut. Steve Thompson also on for Chris Iwelumo.
Fox was booked for a challenge on Murray and referee Grant Hegley was reaching for his pocket five minutes later to send of Edgar after he blocked Norris, earning a second yellow and then a red.
Priskin had the ball taken off his foot after Jaime Peters found him before Norris struck five minutes from time, backheeling the ball in following a corner.
Burnley were level though in the first minute of added on time, Carlisle diverting Alexander's corner into the net to leave the honours even.
Town: Fulop, Peters, McAuley, Smith, O'Connor, Hyam, Leadbitter (Healy 46), Norris, Townsend (Murray 72), Priskin, Stead. Subs not used: Murphy, Eastman, Lambe, Ainsley, Hourihane.
Burnley: Jensen, Edgar, Carlisle, Bikey, Fox, Elliott, Alexander, Marney, Wallace, Paterson (Eagles 67), Iwelumo (Thompson 73). Subs not used: Grant, Cork, McDonald, Cort , Rodriguez. Sent-off: Edgar. Booked: Edgar, Fox.