Forfar are the only team to beat Ally McCoist's side this season - winning 2-1 at Station Park in the Scottish League Cup - but they were narrowly beaten in the league meeting.
The result means that Rangers have won all of their league fixtures this season and are now six points clear of second-placed Dunfermline.
They scored 23 goals in their five games prior to Sunday's game but were forced to take a more functional approach in a game in which Forfar were a force throughout.
The home side made a bright start to the game, with Omar Kader failing to connect properly with a good left-wing cross by Gavin Swankie after timing his run into the box to perfection.
Rangers grew into the contest as it progressed and Lee McCulloch spurned two good opportunities to get a shot away in successive corners midway through the first half.
Forfar played well, though, and Swankie had a snap shot blocked on the edge of the box as the home side competed strongly against the runaway league leaders.
But three minutes before the interval, Rangers found a breakthrough as a poor defensive clearance landed at David Templeton's feet to pick out a pass to Andrew Little, who made no mistake from eight yards.
Nicky Law's weaving run ended with a left-footed chip that beat Darren Hill in the Forfar goal but landed on the roof of the net.
Forfar worked hard to find a way back into the game, Darren Dods seeing his attempt blocked on the line by Templeton as the home side increased their intensity.
Rangers rode their luck in the closing stages when Sebastian Faure almost diverted a cross into his own goal, but they held on for the victory that enhances their bid for the first division title.