Ally McCoist's side moved seven points clear of second-placed Celtic thanks to two goals from Croatian striker Jelavic in the space of eight minutes midway through the second half.
Celtic can close the gap with a win over Hearts later today, but reigning champions Rangers can sit back and relax after inflicting a defeat on new Hibs manager Pat Fenlon in his first home match in charge.
Fenlon had named an unchanged side from the one who saw their game abandoned at Motherwell last week on his managerial debut, while Carlos Bocanegra and Lee Wallace both recovered from injury to start for Rangers.
Hibs had an early chance to put the visitors under pressure with a free-kick 35 yards out which was flighted into the area by Ivan Sproule. Steven Whittaker's headed clearance landed at the feet of Lewis Stevenson, who dragged his shot across the face of goal and narrowly past the post.
Hibs could have snatched the opener on the stroke of half-time when a Sproule ball in the box was completely missed by Wallace and fell for Leigh Griffiths, but he squandered a great chance by firing straight into the grateful hands of goalkeeper Allan McGregor.
Hibs' fans claimed a penalty for handball against Whittaker early in the second half but the pleas were ignored. However, referee Iain Brines did point to the penalty spot at the other end moments later when Wallace was fouled in the box by Michael Hart and Jelavic converted to hand Rangers the lead after 61 minutes.
Hibs should have levelled almost immediately when Paul Hanlon threw himself in front of Sproule's free-kick only to send his diving header over the crossbar when he looked certain to hit the target.
And Rangers doubled their advantage when Jelavic grabbed his second of the day after 69 minutes. Gregg Wylde was the provider with a corner from the left which found the Croatian unmarked in the box, and the striker left goalkeeper Graham Stack no chance with the header.
In the closing stages Rangers goalkeeper McGregor was called into action to claw a deflected cross from Hanlon away from goal before the ball broke for Isaiah Osbourne, who failed to connect properly and bury the rebound.