Leanne Crichton’s side faced an uphill task following the 2-0 reverse in Sweden seven days ago, and it took just under a quarter of an hour for Hammarby here to add a third of the tie.
Despite a valiant display from the Gers, the visitors two more goals after the interval to clinch their place in the next round and end Rangers’ European bid this season.
Attention now returns to league action as Rangers make the trip to face Partick Thistle on Sunday afternoon.
From the team which triumphed in Sunday’s Old Firm encounter, in came Kirsty Smith, Eilidh Austin, Fallon Connolly-Jackson and Hannah Blake.
The onus was on the Gers to start with a purpose, but it was the Swedish outfit who carved out the first opportunity of the contest when Christine Walter’s pull-back was ballooned over the top by Ahgren Sorum from the edge of the penalty area.
Calliste Brookshire then threatened down the opposite end when her delivery was headed out for a corner.
However, the visitors broke the deadlock in Cumbernauld on 13 minutes to leave Rangers with an almighty mountain to climb in the tie.
Hammarby showed their intelligence in creating space in the middle of the pitch, with Luise Janzen slipping a delightful pass into Walter who steadied herself inside the penalty area before arrowing beyond Jenna Fife.
Leanne Crichton’s side sought an immediate riposte when Laura Berry swivelled inside the danger area and her attempted shot cannoned inadvertently off Kirsty Smith.
The forward looked to profit moments later when the away side played their way into trouble deep inside their own half, but her effort was straight down the throat of the Hammarby goalkeeper.
There was no doubting the quality of the Swedish visitors – as they underlined seven days ago in Stockholm – as Marin Hermannsdottir beat Mijke Roelfsema all ends up on the far side touchline before racing into the penalty area and lifting her finish off target.
Walter menaced down the left once again just before the interval, but Fife did well to read the winger’s intentions on the cross and smother at her near post.
The second half began with Hammarby utilising a familiar route through the dangerous Walter, with her dangerous cut-back towards Vilde Hasund at the far post almost swiped goalwards by the winger.
Berry then showed tremendous endeavour down the right before advancing towards the penalty area, but after chopping onto her unfavoured left side her finish was tame and into the arms of the Hammarby goalkeeper.
And the away side put the tie beyond doubt on the hour-mark when Hermannsdottir raced clear down the right and, with only Fife to beat, curled her finish around the goalkeeper and into the bottom corner.
A third of the night was added with just over ten minutes remaining when substitute Fanny Peterson was on hand to stab home on the rebound after a terrific initial save from Fife.
RANGERS: Fife, Smith (Hendle, 62), Austin, Roelfsema, Docherty, Connolly-Jackson (Boyce, 62), Cruft (Black, 72), Blake, McLeary, Brookshire (Wilkinson, 72), Berry (Hay, 72)
Subs not used: Rarity, Collins, Hill, Miller, Thrysoe
HAMMARBY IF: Christensen, Arnardottir, Sorum, Walter, Koivisto, Janzen, Reidy, Lennartsson, Karlsson, Hermannsdottir, Hasund
Subs: Holmgren, Pegram, Rosendal, Lorenius, Rehnberg, Linder, Persson, Nylen, Peterson, Olsson, Hedlund
