The loss at Loftus Road in London means that John Carver’s side remain in danger of getting relegated to the Championship.
Joey Barton had the first chance of the game, when he tried a long-range attempt in the 14th minute.
Remy Cabella came close for Newcastle just five minutes later when he latched onto a pass from Moussa Sissoko and shot on goal, but his effort was saved.
Ryan Taylor, Ayoze Perez, Sissoko and Fabricio Coloccini had chances during the remainder of the first half, but it was Rangers who scored the second goal of the game.
Matthew Phillips restored parity for the hosts in the 54th minute when he headed home from a Charlie Austin cross.
Then just past the hour mark, Leroy Fer fired home from outside the Newcastle penalty area after being teed up by Matthew Phillips.