The FA Cup semi-finalists had Jeff Whitley sent off in the 60th minute for violent conduct, but took the lead only for Preston to hit back and grab a last-minute equaliser.
Substitute Sean Thornton hammered home a brilliant free-kick in the 70th minute to restore the Black Cats lead only for defender Tyrone Mears to equalise in the 79th minute.
Sunderland went ahead again in the 84th minute from the penalty spot. Marcus Stewart was brought down by Rob Edwards and the Black Cats' leading scorer calmly sent Andy Lonergan the wrong way with his spot-kick.
Preston piled on the pressure and only a brilliant save by Mart Poom prevented Eddie Lewis from equalising in the 89th minute, but with the game into injury time, Lewis curled a superb free-kick into the top corner to equalise.
There had been no hint of the second-half drama as the teams had been evenly matched in the opening 45 minutes.
The visitors created better chances, only to fall behind in the 25th minute to an unfortunate own goal.
Kevin Kyle hoisted a hopeful ball into the middle only for Mears to slice the ball into his own net in attempting to clear.
John Oster had already had the ball in the net in the 19th minute only for his header to be ruled offside.
Preston hit back and, after Poom had punched out a free-kick from Mears, Gary Breen cleared off the line from Simon Lynch's angled drive.
Healy then pulled his close-range shot across the face of goal and Ricardo Fuller squandered a great chance by wanting too much time.
Healy however finally hauled Preston level in the 43rd minute. Sunderland appealed in vain for a penalty when Kyle was clearly held. Play immediately switched to the other end and Healy, with his back to goal, turned smartly to squeeze the ball into the net via the base of the upright.