Former Galatasaray boss Souness was returning to Turkey along with former Gala keeper Brad Friedel and former international stalwart Tugay.
The home side included former Sunderland defender Baki Mercimek in their starting line-up, while one-time Bolton midfielder Akin Bulent was on the bench.
The opening minutes offered precious little by way of goalscoring chances, until Mustafa headed weakly at Friedel from eight yards out.
After 20 minutes Vratislav Gresko curled a free-kick just wide, as Rovers held their own in terms of possession, before Deniz headed wide on the half hour from Abdel El Saka's cross.
Shortly afterwards, Serkan's header clipped the top of the crossbar following a ball in from the right from Josip Skoko.
The Australian then gave the home side the lead three minutes before the break, as Friedel came out to head clear and Skoko returned a superb 35-yard half-volley back into the empty net.
Within a minute it was 2-0 as Deniz played in Souleymane Youla, who rifled a 15-yard right-footer under the despairing Friedel.
Rovers brought on Andy Cole at half time and home defender Umit almost sliced the ball into his own net soon afterwards.
Cole then threw his side a lifeline as he wriggled clear on the left, drew sub keeper Damir Botonjic and played in Brett Emerton for a simple finish from eight yards.
However, just before the hour a long ball over the top allowed Youla to race clear of Markus Babbel and Lorenzo Amoruso and drive his shot past Friedel from 15 yards.
Rovers made a double change to try and grab another away goal and as time ticked away one of the subs, Corrado Grabbi, volleyed over from eight yards as Souness' men left themselves a massive task in the second leg.
Genclerbirligi: Tokgoz, Daems, El Saka, Ozkan, Youla, Bozkurt, Skoko, Tandogan, Mercimek, Baris, Balci. Subs: Botonjic, Ozbey, Akin, Basturk, M'Bayo, Cihan, Karaman .
Blackburn: Friedel, Neill, Amoruso, Babbel, Gresko, Emerton, Tugay, Baggio, Thompson, Jansen, Yorke. Subs: Kelly, Martin Taylor, Cole, Reid, Johansson, Gallagher, Grabbi.
Referee: Paolo Vertini (Italy)