Rangers booked their place in the third qualifying round of the Europa League despite a 1-1 draw with Osijek on Thursday, winning 2-1 on aggregate.
Alfredo Morelos' goal in Croatia had given Steven Gerrard's men the advantage and a single Nikola Katic goal proved enough once more at Ibrox, even if a late Borna Barisic drive set up a tense finish.
Both sides struggled to truly test the goalkeepers in the first half, with most shots on target fired straight at Marko Malenica or Allan McGregor.
The goal eventually arrived eight minutes into the second half.
A whipped ball into the box from James Tavernier was headed back across goal by Morelos, with Katic on hand to nod home.
Barisic pulled one back for the visitors in the 89th minute but they could not find the second away goal that would have snatched the aggregate victory.
The result means Rangers will face Maribor in the next round, following a 2-0 aggregate win for the Slovenian side against Chikhura Sachkhere.