James Tavernier and Lassana Coulibaly netted second-half goals as Rangers recorded a 3-1 victory over Maribor in the first leg of their Europa League third qualifying round tie at Ibrox on Thursday night.
Alfredo Morelos had sent Rangers ahead before Gregor Bajde levelled, but Tavernier netted a penalty early in the second period before Coulibaly registered late on to ensure that Steven Gerrard's side would take a two-goal lead into next week's second leg in Slovenia.
The response from Maribor was impressive, however, and Allan McGregor had to make a flying save to keep out a Aleks Pihler strike in the 14th minute, before two excellent challenges from Tavernier denied Bajde as the first half progressed.
Rangers thought that they had doubled their lead in the 39th minute when Morelos netted once again, but the linesman had his flag raised, and it was Maribor that were to grab the game's next goal.
The leveller arrived in the 40th minute - Slovenian attacker Bajde finding a route past McGregor with a strike from the edge of the box to silence the home crowd.
Rangers started the second period brightly, however, and were awarded a penalty in the 49th minute when Coulibaly was chopped to the ground by Sasa Ivkovic.
Rangers captain Tavernier was given the responsibility of taking the spot kick, and the defender found the back of the net with a smart finish to ensure that the Scottish giants took a 2-1 lead on home soil.
Tavernier almost notched his second in the 53rd minute with a curling effort that looked to be finding the back of the net, but Handanovic was on hand to produce a super save.
Connor Goldson fired over the Maribor crossbar in the 71st minute as Rangers looked for a third, and it ultimately came in the 86th minute when Coulibaly bundled a Jamie Murphy cross into the back of the net.
Rangers will continue their Scottish Premiership campaign with a home match against St Mirren on Sunday afternoon.
RANGERS (4-3-3): McGregor; Tavernier, Katic, Goldson, Flanagan; Coulibaly, Ejaria (Murphy 78'), Arfield; Kent (Mccrorie 87'), Morelos (Sadiq 87'), Candeias
MARIBOR (4-4-2): Handanovic; Kilnar, Ivkovic, Suler, Viler; Bajde (Mesanovic 62'), Vrhovec, Dervisevic, Pihler; Tavares (Vrsic 79'), Zahovic