With their rivals not in action this weekend — Celtic’s Scottish Cup tie at Inverness was postponed — the Scottish champions were well aware of the importance of taking maximum points.
El-Hadji Diouf’s opener was cancelled out by Jamie Hamill from the penalty spot but it was Tim Clancy who had the final say when he was unfortunate enough to net an own goal late on.
Rangers pushed forward in search of the opener and Manuel Pascali almost unwittingly handed them the lead when he came close to forcing a Madjid Bougherra cross into the back of his own net.
The breakthrough came after 38 minutes when Diouf netted his first goal at Ibrox to hand Rangers the advantage. Steven Whittaker supplied the pass and Diouf took a touch before rifling a right-foot shot past the grasp of the Kilmarnock goalkeeper and into the bottom corner from 10 yards.
Rangers could have doubled their lead shortly after the restart when Nikica Jelavic snatched the ball from the feet of Mohamadou Sissoko and decided to have a crack at goal himself, instead of picking out another blue jersey in the box. But Jaakkola did well to stand up to the angled drive and blocked well at his near post.
Kilmarnock were level terms after 60 minutes when referee Alan Muir ruled that Bougherra had fouled Clancy in the box and Hamill stepped up to blast the penalty high into the net.
Rangers were back in front with three minutes left when Vladimir Weiss flighted a dangerous cross into the box and Clancy inadvertently bundled the ball into his own net.
Rangers boss Smith said: “I said before the St Mirren game last week that we had two very important league matches. It was important we got wins in these two games for that reason and I’m delighted we have done.”