The Gers flew out the gates and Kieran Dowell wasted no time in getting on the scoresheet as he found the back of the net after four minutes.
Allowing Motherwell very little joy in the early stages, Rangers made it 2-0 after just 16 minutes through Todd Cantwell.
The home side carved out a few chances, but were unable to seriously test Jack Butland in the first period.
After the break, Motherwell were able to apply more pressure on Rangers - who were happy enough to absorb it.
The Gers slowed their pace in the second half and focused on controlling the ball when in possession, perhaps aiming to avoid potential injuries.
Motherwell continued to struggle to carve out any real opportunities to challenge Butland and heads began to drop.
Cyriel Dessers, who assisted Dowell in the first period, found the back of the net seven minutes from time and again in time added on, but both were ruled out for offside.
The win puts Rangers just two points behind rivals and league leaders Celtic, with a game-in-hand.
