They did so thanks to a stunner from Ryan Jack – a 20-yard volley that flew into the top corner after 36 minutes.
Steven Gerrard was without Kemar Roofe and Alfredo Morelos – both suspended, but Scott Arfield and Jermain Defoe recovered from injury to take a place on the bench.
After a level start between Gerrard’s team and Killie, under new boss Tommy Wright, Jack sent Rangers ahead and despite a bright start to the second half they were unable to add to the scoresheet – and Joe Aribo spurned a gilt-edged chance with six minutes to play.
Both sides had claims for penalties – James Tavernier bundled down inside the box in the first half and Rory McKenzie tumbling beside Leon Balogun late on at the edge of the same area.
Regardless Rangers saw out the win to re-establish their advantage at the top of the table and Arfield was given a late run on his return from injury with one eye on Thursday’s Europa League trip to Royal Antwerp.
Here’s how the Rangers players rated...
Player ratings scale - 10: One of the best performances you've seen. 9: Outstanding. 8: Very good. 7: Good. 6: Average. 5: Poor, 4: Very poor. 3: A terrible day at the office. 2: Abysmal. 1: One of the worst performances you've seen
Get a year of unlimited access to all The Scotsman's sport coverage without the need for a full subscription. Expert analysis of the biggest games, exclusive interviews, live blogs, transfer news and 70 per cent fewer ads on Scotsman.com - all for less than £1 a week. Subscribe to us today
9. Ianis Hagi - 7
Went close with free-kick just before half-hour. Not his finest game but persistence pays off and always had a role in Rangers' one-touch build-up play. Photo: Alan Harvey - SNS Group
10. Ryan Kent - 8
Divides opinion but all that was missing from Kent's afternoon was a goal. Repeat performances over a run of games and detractors will fall away and goals will surely come too. Should have scored on break just before half-time. Photo: Rob Casey - SNS Group
11. Cedric Itten - 8
Led the line but looks more of a foil for a partner. Great space making turns round the corner and size causes defenders problems, but like Kent goals are missing despite positive link-up play. Photo: Craig Foy - SNS Group
12. Steven Gerrard
All round good performance against a difficult opponent and saw his side bounce back after last weekend's disappointment Photo: Rob Casey - SNS Group