An own-goal from Alex Keddie and a Nikica Jelavic penalty sealed the victory at Ibrox on Saturday as the Scottish champions held on after Joe Cardle pulled a goal back for the Pars.
The win followed a goalless draw with St Johnstone and a first league defeat of the season against Kilmarnock, as Rangers moved seven points clear of Celtic ahead of their meeting with Dundee United on Sunday.
Thomas Bendiksen made his first competitive start for Rangers after impressing in the midweek friendly against Hamburg, where he netted for the Light Blues.
The Norwegian midfielder was drafted into the side for the clash with the Pars, along with Kyle Bartley and Gregg Wylde, who returned from suspension.
Ross Perry, Lee McCulloch and Kyle Lafferty - who had been struggling with a back problem earlier in the week - were dropped to the bench.
Dunfermline were without Paul Burns and Nick Phinn for the visit to Glasgow after both were added to the club's lengthy injury list following last week's 3-3 draw with Aberdeen.
A minute's silence for Gary Speed turned into a minute's applause at Ibrox ahead of kick-off.
Once the match was under way, Sone Aluko - making his home debut - embarked on a surging run down the right flank before setting up Jelavic but the striker blasted high and wide from six yards.
The Croatian was threatening again when he connected with a Steven Davis pass and bulleted a header narrowly past the upright as Rangers piled on some early pressure.
Aluko then had a go himself from just inside the box but rifled over before Wylde drew a decent save from goalkeeper Paul Gallacher.
Rangers' pressure paid off when they took the lead after 21 minutes.
Wylde punted the ball into the box for Bendiksen and Gallacher's attempted clearance cannoned off the body of team-mate Keddie and into the back of the net.
The home side doubled their advantage seven minutes later when Aluko was tripped in the box by Gary Mason and referee Steve Conroy pointed to the penalty spot before Jelavic confidently lashed home.
However, Dunfermline pulled a goal back with 31 minutes gone after Cardle's solo run ended with a low shot past the grasp of Allan McGregor.
At the other end, Davis tested Gallacher with a well-struck shot before Wylde dragged his effort past the upright.
Rangers started the second half strongly and Bartley came close with a shot that was deflected just over the crossbar, before Jelavic nodded wide of target.
Bendiksen left the pitch to rapturous applause from the crowd when a decent shift came to an end after 58 minutes and he was replaced by Lafferty.
Jelavic looked hungry for more goals and he was unfortunate not to have the net bulging again when a full-stretch Gallacher managed to tip his effort just past the post.
Rangers looked the more likely of the two teams to find the back of the net again and Lafferty threw himself in front of an Aluko cross only to see his header blocked by the goalkeeper.
Both players combined well again moments later but, on this occasion, Lafferty fired across the face of goal and just wide.
Aluko then tried his luck with an opportunistic shot from distance that floated past the upright, before Keddie nodded just over the crossbar from a corner for the Pars late on.