Rangers have work to do in their Europa League third qualifying round tie after defensive lapses were punished by triumphant Jagiellonia Bialystok in Poland.
Kajetan Szmyt scored a first-half double to capitalise on an error-strewn display from Derek McInnes' side in the opening 45 minutes of the first leg.
Despite a dream start for the visitors, when Tuur Rommens drilled a low cross that zipped through a tangle of legs before cannoning over the line off home defender Guilherme Montoia, Rangers failed to get a hold of the game.
Their goal was wiped out by a soft concession. Szmyt dragged his side forward wide on the left and worked an angle for a cross that evaded everyone and sneaked in at the far post past the outstretched Ivor Pandur.
The hosts struck again within 10 minutes following a counter-attack that started on the edge of their own area after Thelo Aasgaard tried a spinning flick, much to his manager's chagrin.
Emmanuel Fernandez slipped as he tried to block the subsequent cross and Pandur made a strong initial save, but Szmyt doubled his haul by following up sharply to fire in the rebound.
A mix-up between Dujon Sterling and Fernandez allowed the home side the chance for a third, but Rodrigo Conceicao opted to blast wide instead of sliding across the area for an almost certain goal.
Rangers looked all over the place for much of the first period, prompting McInnes to make three half-time changes. The introduction of Cammy Devlin, Findlay Curtis and the sought-after Nicolas Raskin gave them a much better foundation.
Szmyt went close to a hat-trick with a shot straight at Pandur, and Spaniard Jesus Imaz skewed a first-time attempt wide after another swift counter-attack.
But Rangers finished strongly and Ross McCrorie had a powerful drive well blocked, substitute Lawrence Shankland's effort was smothered a yard out then Curtis' stoppage-time volley rattled the post.
