There was little to separate the sides throughout the 90 minutes on a crisp October afternoon in Milngavie, with Ross McCausland levelling proceedings with a well-taken finish midway through the first half.
However, Breidablik breached the Gers’ rearguard twice more before the half-time interval to put themselves into a commanding position and, despite a late Connor Allan strike, the Light Blues found themselves on the wrong side of the margins at full-time.
David McCallum’s side were boosted by the inclusion of Danilo, Ben Davies and Leon Balogun in the starting lineup, with the former two playing 45 minutes as they continue their recovery from recent injuries.
And the Light Blues began the match on the front foot as Leon Balogun showed all his experience to step through the Briedablik press before firing a pass into Cole McKinnon. The 20-year-old swivelled and released Danilo just inside the away side’s half, with the Brazilian’s audacious lob from distance caught by Einarsson.
Rangers continued to bristle with an intent in the opening exchanges, going agonisingly close to breaking the deadlock when Ross McCausland cut inside and rifled a left-footed effort which the Breidablik goalkeeper tipped onto the crossbar.
However, the Gers suffered a setback eight minutes into the contest as Jason Dadi Svanporsson tapped home at the far post from a David Ingvarsson driven cross to give the visitors an early buffer.
Danilo and McKinnon then combined in the final third as the home side searched for a riposte, but the latter could not bring the ball under control amid pressure from an opposing defender.
The Icelandic side threatened down the opposite end moments later as the goalscorer Svanporsson found space in the penalty area before heading over from Gisli Eyjolfsson’s cross.
Rangers’ pressure told just beyond the half-hour mark as a move of sheer quality cut Breidablik open to provide the equaliser. Bailey Rice lifted his head in space in midfield and guided a deliciously lofted ball through to McCausland who had beaten the offside trap, with the Northern Irishman showing terrific composure to lift his finish over the goalkeeper.
However, such was the quality of the Europa Conference League opposition that they always carried a threat in attacking transition, restoring their advantage moments later as Klaemint Olsen, an early first half substitute, finished beyond Robby McCrorie from close range.
And just as the half looked as if it would meander towards its conclusion, Rangers found themselves having to contend with a two-goal deficit heading into the dressing room. The dangerous Ingvarsson collected the ball on the left-hand side before firing a delivery into Svanporsson whose effort was tipped onto the post by McCrorie, but Eyjolfsson reacted first for Breidablik to slam home the rebound.
The half-time interval prompted a quadruple substitution as the minutes of several first-team players were managed, with Kieran Wright, Johnly Yfeko, Archie Stevens and a trialist entering the fray.
Indeed, Stevens, who recently represented England at Under-18s level, almost made an immediate impact as he collected a pinpoint Balogun lofted pass out of defence, working the ball onto his favoured right-foot for a shot inside the penalty area but being denied by a reflex stop from Brynjar Atli Bragason.
The Light Blues were certainly playing with a spring in their step despite the scoreline, threatening again on 49 minutes when McCausland drifted inside and switched the point of attack to Arron Lyall in space. The 20-year-old looked to manufacture space for an effort, although his left-footed finish was planted into the side netting.
Rangers scarcely looked threatened from a defensive sense as the match ticked over the hour-mark, but puncturing a resolute Breidablik defence was proving difficult as they searched for a route back into the contest.
Opportunity beckoned for Lyall with 18 minutes remaining as he pulled into space at the edge of the penalty area, receiving a pull-back from Adam Devine who had burst into the danger area, but the midfielder could not keep his effort under the crossbar.
James Graham was one of three players introduced with a quarter of an hour remaining, threatening the Breidablik rearguard when he was slipped in-behind by Stevens before the onrushing Bragason raced off his line to thwart the danger.
Optimism was briefly restored for Rangers in stoppage time when substitute Connor Allan met Lyall’s corner at the near post, rifling a powerful volley under the Breidablik goalkeeper to reduce the arrears.
However, it was too little, too late for the Gers in terms of the scoreline, with the referee bringing a competitive contest to an end shortly after.
RANGERS B: McCrorie (Wright, 45), Devine, Balogun (Allan, 75), Davies (Yfeko, 45), Fraser, Rice (Hutton, 87), King (Trialist, 45; Nsio, 71), McKinnon (McInally, 75), McCausland (Graham, 75), Lyall, Danilo (Stevens, 45)
BREIDABLIK: Ari Einarsson (Bragason, 45), Muminovic (Adalsteinsson, 75), Sigurdarson (Sigurjonsson, 57), Gunnlaugsson, Karl Einarsson (Stefansson, 87), Steindorsson (Olsen, 30), Eyjolfsson (Hlynsson, 57), Ludviksson (Yeoman, 75), Svanporsson (Fjeldsted, 63), Margeirsson, Ingvarsson (Orrason, 87)
REFEREE: Thomas Denholm