Captain Lee Wallace's struck to give the home side the lead just after the quarter-hour mark.
And Martyn Waghorn doubled their advantage shortly before the break, turning in Barrie McKay's pass.
Nicky Law added a third with a shot high into the net as Mark Warburton's side claimed their tenth win in all competitions.
Having scored five goals in each of their last three matches, Rangers were keen to maintain their impressive goal haul but their second half performance failed to match the tempo displayed in the opening 45 minutes.
The hosts were unchanged for the first time this season and in-form Waghorn quickly garnered their first scoring opportunity with barely five minutes gone as he pounced on a defensive error to test Darren Jamieson but the goalkeeper reacted well.
Livingston, the only side in the Championship without a league win this season, responded with their first chance when a Myles Hippolyte free kick found the head of Declan Gallagher but his header picked out keeper Wes Foderingham.
It was from a free-kick that Rangers took the lead after 16 minutes The pre-planned move broke down but the ball rebounded to Wallace who, from 30 yards, struck the ball cleanly with his left foot low in to the bottom corner for his fourth goal of the season - equalling his tally for last season.
Livingston were without the suspended Ben Gordon and lost his replacement Craig Sives to injury inside 25 minutes, with Morgyn Neill replacing him. The bottom side did not dwell on their misfortune and only a flying save from Foderingham kept out Liam Buchanan's powerful shot.
Rangers, fuelled by the guile of Nathan Oduwa and the lively front play of Waghorn, dealt Livingston a decisive blow five minutes from half-time.
Oduwa was involved in the build-up, Waghorn holding up the ball and rejecting all passing options to work his way free and precisely angle a low shot beyond Jamieson.
If a second half onslaught was expected it did not appear as Rangers failed to match their earlier intensity while Livingston never gave up but never seriously threatened the home goal.
Kenny Miller, who appeared as a substitute in the first ever meeting of these sides in 2001, came off the bench and slid a pass into the path of fellow substitute Law who angled his shot high into the net for his first goal of the season.
Match ends, Rangers 3, Livingston 0.
Second Half ends, Rangers 3, Livingston 0.
Attempt missed. Myles Hippolyte (Livingston) left footed shot from the left side of the box is just a bit too high.
Kenny Miller (Rangers) is shown the yellow card for a bad foul.
Foul by Kenny Miller (Rangers).
Myles Hippolyte (Livingston) wins a free kick in the defensive half.
Substitution, Livingston. Kieran Gibbons replaces Scott Pittman.
Nicky Law (Rangers) wins a free kick on the right wing.
Foul by Darren Cole (Livingston).
Delay in match  (Livingston).
Attempt missed. Dean Shiels (Rangers) left footed shot from the centre of the box is close, but misses to the left.
James Tavernier (Rangers) wins a free kick on the right wing.
Foul by Myles Hippolyte (Livingston).
Attempt blocked. Nathan Oduwa (Rangers) right footed shot from outside the box is blocked.
Foul by Nicky Law (Rangers).
Gary Glen (Livingston) wins a free kick in the attacking half.
Foul by Rob Kiernan (Rangers).
Daniel Mullen (Livingston) wins a free kick on the left wing.
Goal!  Rangers 3, Livingston 0. Nicky Law (Rangers) left footed shot from the centre of the box to the high centre of the goal. Assisted by Kenny Miller.
Nathan Oduwa (Rangers) wins a free kick in the attacking half.
Foul by Darren Cole (Livingston).
Scott Pittman (Livingston) is shown the yellow card for a bad foul.
Rob Kiernan (Rangers) wins a free kick in the attacking half.
Foul by Scott Pittman (Livingston).
Dean Shiels (Rangers) wins a free kick on the right wing.
Foul by Hugo Faria (Livingston).
Hand ball by Daniel Mullen (Livingston).
Substitution, Rangers. Dean Shiels replaces Gedion Zelalem.
Foul by Lee Wallace (Rangers).
Gary Glen (Livingston) wins a free kick in the attacking half.
Corner,  Livingston. Conceded by Lee Wallace.
Substitution, Livingston. Daniel Mullen replaces Liam Buchanan.
Foul by Kenny Miller (Rangers).
Myles Hippolyte (Livingston) wins a free kick in the defensive half.
Attempt missed. Nicky Law (Rangers) right footed shot from the centre of the box is too high.
James Tavernier (Rangers) wins a free kick on the right wing.
Foul by Jackson Longridge (Livingston).
Foul by Lee Wallace (Rangers).
Hugo Faria (Livingston) wins a free kick in the attacking half.
Nathan Oduwa (Rangers) wins a free kick in the defensive half.
Rangers made it six wins out of six in the Scottish Championship with a comfortable victory over Livingston.