Alfredo Morelos proved the difference as Rangers secured a valuable 3-1 first-leg advantage over Maribor in the UEFA Europa League third-qualifying round.
The Colombian striker scored the opener and won the penalty for James Tavernier's second-half spot-kick before Lassana Coulibaly capped off a victory that puts Steven Gerrard's men in the driving seat for next week's return clash.
Rangers, however, will have to avoid a stumble in Slovenia after giving up an away goal in the shape of Mitja Viler's 40th-minute equaliser.
All eyes were on Morelos after his controversial dismissal in last weekend's Scottish Premiership draw at Aberdeen – a red card that was rescinded during the week – and he did not disappoint, bundling home at point-blank range in the sixth minute after Jasmin Handanovic failed to hold Ryan Kent's initial effort.
An offside flag prevented the 22-year-old from doubling his tally shortly before half-time and Rangers's frustration was immediately compounded as, at the other end, Viler finished well from the edge of the area.
Any sense of tension at Ibrox, though, was relieved five minutes after the interval.
Morelos went down under a challenge from Sasa Ivkovic and captain Tavernier, who also converted from the spot against Aberdeen, stepped up to stroke his side back into the lead.
Rangers grew in confidence with the goal and created several opportunities to extend the margin, while Kent had appeals for a penalty waved away by the referee.
And a third finally came in the 86th minute, Coulibaly diverting in Jamie Murphy's cross from the left to set Rangers firmly on their way to the play-off round.