The Light Blues were made to sweat for the victory, which was played in the baking heat of southern Spain, with 16-year-old Laura Berry finishing off a terrific team move to secure the victory.
There was a late change to the Light Blues lineup as Megan Bell replaced a trialist, with Rangers making a positive start to proceedings in possession.
It was Levante, however, who fashioned the first shot in anger as Andonova tested her luck from 30 yards out that Jenna Fife watched sail over her crossbar.
Sosa Martin was next to take aim at the Rangers goal, although her driven effort was deflected comfortably behind for a corner.
Clear-cut opportunities were few and far between for the Light Blues in the early exchanges, with Rio Hardy slightly overcooking a pass as she looked to release Jodi McLeary into an advanced area down the left.
The 25th minute mark proved the cue for the first water break of the evening, with Kathryn Hill putting her body in front of a curling effort from Daniela as the home side advanced into the final third.
Rangers responded with their best moment of the game until that point on 35 minutes. Rachel Rowe did exceptionally well to hold the ball in the Levante half, bringing Brogan Hay into the action with a pinpoint diagonal pass.
The Gers winger showed nimble footwork to accelerate to the byline, standing up a cross for McLeary at the far post which was blocked away for a corner.
Rowe then met Bell’s subsequent delivery from the right on the volley, although she could not keep her powerful effort under the crossbar.
Jo Potter would have been pleased with the persistence of her side in continuing to build patiently from defence, with Levante going man-for-man in their attempts to stem Rangers.
Half-time then prompted a double switch from the Gers boss as Tessel Middag and Mia McAulay replaced Hill and Bell.
The Gers almost capitalised on a mistake from the Levante goalkeeper within 90 seconds of the start of the second half, with Hardy unfortunate not to bring the loose pass under control inside the penalty area.
The upright rattled three minutes later when Rowe went agonisingly close to breaking the deadlock. Picking up the ball just inside the Levante half, she drove menacingly into the final third despite having her shirt tugged, before unleashing a driven effort from 25 yards which cracked the inside of the post.
The Spanish side responded with opportunities of their own before the hour-mark. Fife was quick off her goalline to thwart Aixa Salvador, before Alharilla dragged her shot wide of the Gers goal after being played through down the right-hand side.
Levante brought an entirely new team onto the pitch just prior to the second water break of the match, with Rangers soon getting their noses in front in the match.
A magical piece of footwork from Jodi McLeary manufactured space inside the penalty area, before she slipped Hardy through on goal. Lifting her head, the forward spotted an unmarked Laura Berry from close range and the substitute tapped home to give Rangers the lead in Spain.
The Gers almost doubled their advantage through another 16-year-old as McAulay skipped inside from the left-hand side before firing over Holgren’s upright.
Levante almost equalised when a deep free-kick ricocheted around the danger area, but Rangers cleared the danger to seal the victory and round off a productive week in Spain.
LEVANTE UD: Holgren, M, Mendez, Fernandez, Andonova, Martin, Banos, Daniela, Alharilla, N. Mendoza, Paula, Rizo
SUBS: Alvarez, Salvador, Arce, Soriano, Carlota, Bascu, Gonzi, Carolina, Secades, De La Fuente, Gabaldon
RANGERS: Fife, McLauchlan, Hill (Middag, 45), Docherty, Hay (Austin, 90), Cornet, Maclean, McLeary, Rowe (Berry, 61), Hardy, Bell (McAulay, 45)
SUBS NOT USED: Colson, Jardine, Clark