Birmingham 0 Blackburn 4
The home side dominated play for long spells, but were undone by goals on 66 and 68 minutes by Barry Ferguson and Lucas Neill respectively and a cracker from Tugay and a late effort from Paul Gallagher.
Birmingham will surely rue missed chances, as Rovers were under the cosh for long periods, but Graeme Souness' side weathered the storm to snatch victory.
Blues should have gone in front on seven minutes but Stan Lazaridis headed over from six yards.
Christophe Dugarry, who had a bad afternoon, was guilty of one of the misses of the season as he scooped over the bar from a yard out when it looked easier to score.
Robbie Savage crafted an opening for Birmingham but no-one was on hand to convert, while Mikael Forssell then shot wide on the stroke of half time.
Forssell then had a goal disallowed, after Dugarry had committed a foul when teeing up his partner, and Blues were made to pay as Rovers took their chances.
Andy Cole was the architect of the opener, threading a superb ball into the path of Ferguson who showed real composure to slot past Maik Taylor.
Birmingham hardly had time to regroup before Neill had put the game beyond them with an unerring finish, but Cole deserved praise again for a superb threaded pass.
Birmingham chased the game but any hopes they had of rescuing the match were ended when Dugarry was shown a second yellow card following a wrestling match with Craig Short.
Turkish star Tugay then scored the goal of the game five minutes from time, smashing into the top corner from 25 yards, and Paul Gallagher put some gloss on the scoreline with his first Premiership goal for Rovers.