Naismith grabbed his ninth goal of the season, before Jelavic – rated doubtful ahead of the game – doubled the advantage just a few minutes after coming off the bench.
The win allowed Rangers to stretch their lead over second-placed Motherwell to nine points.
Jelavic had been struggling with a bug over the weekend and was named among the substitutes for Rangers, with Kyle Lafferty handed the role of lone forward.
Hearts named an unchanged side for the fourth consecutive game for the visit of the Scottish champions.
Rangers carved out the best of the chances during a frantic opening spell and Lee McCulloch was not too far away with a shot from distance that flashed just past the post.
Maurice Edu then saw his effort deflected wide for a corner and the American connected well with a Steven Davis ball into the box only to hook over on this occasion.
Steven Whittaker had a large part to play in the opening goal when he embarked on a surging run before setting up Naismith to rifle into the back of the net after 21 minutes.
Rangers continued to push forward in search of a second goal and a Davis corner broke for Edu on the edge of the box but he lashed over, with Marian Kello untroubled in the Hearts goal.
There was a nervous moment for Rangers when a Carlos Bocanegra clearance, under pressure from Ryan Stevenson, trickled just past the post and narrowly avoided being an own-goal.
Goalkeeper Allan McGregor then produced a superb save to deny Rudi Skacel just before the break.
There was concern for Rangers early in the second half when Bocanegra was caught full in the face by an Eggert Jonsson strike but the defender was able to return to the action after receiving treatment.
Jonsson then tested McGregor with a shot at the near post that the goalkeeper spilled and the offside flag was raised by the time Stevenson pounced on the rebound which was hooked to safety by Bocanegra.
Hearts had another chance to haul themselves level but Skacel drilled wide when he should at least have hit the target.
Rangers made a double change after 71 minutes when Gregg Wylde and Jelavic were thrown into the action for Sasa Papac and Lafferty.
And Jelavic added his name to the scoresheet just three minutes later when he met a Bocanegra ball and sidefooted past Kello from six yards.
Hearts should have pulled a goal back almost immediately but McGregor did well to block two point-blank strikes from Stevenson.