An early goal from Dado Prso gave them a valuable three points, but opportunities were few and far between in a contest that never rose above mediocre.
The defeat leaves Dunfermline joint-bottom of the league with Livingston and they face a struggle to hang on to their top league status.
Rangers wasted no time in imposing themselves on the game and won a couple of corners in the opening two minutes.
Barry Ferguson tested Derek Stillie with a left-foot shot which the goalkeeper could not hold, but his defence came to his aid before Nacho Novo could take advantage.
Ian Campbell then made a great tackle to prevent Prso cashing in on Novo's through pass.
But Rangers moved in front in the seventh minute from their third corner. Dunfermline failed to clear their lines and Fernando Ricksen crossed for Prso to head home.
Dunfermline tried to hit back and Noel Hunt directed a header straight at Ronald Waterreus.
Ferguson and Ricksen had a firm grip on midfield as Dunfermline were restricted to attempts from distance.
Darren Young tried his luck from 25 yards, but Ronald Waterreus was well positioned to save and the goalkeeper also did well to deal with another effort from Hunt from outside the box shortly afterwards.
Novo should have put Rangers two in front midway through the first half after some suicidal defending from Dunfermline, but he dragged his shot wide of the far post.
There was another close call for Dunfermline after 32 minutes when Ricksen shredded the Dunfermline defence, but Thomas Buffel's final effort went agonisingly wide with Novo just short of connecting at the far post.
Rangers were looking for a second before half-time but it was Dunfermline who almost equalised seven minutes from the break.
Darren Young crashed in a 20-yard shot which beat Waterreus but struck the inside of the post and broke to Hunt who shot over.
A sweeping move from Rangers at the start of the second half almost brought reward when Prso laid the ball back for Ferguson just his shot flashed just over the top.
Rangers had claims for a penalty waved away after Buffel looked to be tugged back by Campbell.
Alex McLeish's side did not get things all their own way and Prso was both booked for dissent after a challenge from Campbell as the game became bogged down into a midfield scrap.
Prso had an opportunity with 17 minutes left, but his control let him down at the vital moment.
But Dunfermline never really threatened Waterreus in the closing stages and Rangers were just worth the three points.