Mark Hughes' side had hit back from conceding the opening goal on the half-hour, with strikes from Robbie Savage and Benni McCarthy giving Rovers a half-time lead.
The opening period of the game was notable only for floodlight failure that held up the game for several minutes, but when play resumed striker Alexander Zickler gave Salzburg the lead.
The German latched on to a Christian Tiffert pass to finish decisively past Rovers keeper Brad Friedel.
However, the visitors hit back within two minutes as Savage curled home a glorious free-kick from 25 yards after David Bentley had been fouled.
Seven minutes later Rovers were in front as home keeper Timo Ochs spilled a Morten Gamst Pedersen free-kick and McCarthy pounced to net his second goal in four games.
After the restart, Blackburn could have added a crucial third goal, but Zurab Khizanishvili and Bentley spurned chances, before Savage hoisted his shot over from close range following Pedersen's pass.
That proved to be crucial as Salzburg powered forward in the closing stages.
Friedel made a superb save from Niko Kovac's header with six minutes left on the clock, but the Croatian then played a large part in his side's last-gap leveller.
His cross was met by towering striker Marc Janko, a half-time substitute, whose header left Friedel well beaten.