A first win of the season lifted the R's off the bottom last week, but struggling Newcastle were also in desperate need of three points and an 81st minute strike from substitute Ameobi rewarded their dogged display at a damp St James' Park.
The hosts went in search of an early opener, but Papiss Cisse could not direct his back-post header on goal and he then failed to find strike partner Demba Ba with a wayward cross.
Magpies winger Jonas Gutierrez was similarily wasteful when he overhit his centre from a promising position, while the R's gave a glimpse of their threat as Adel Taarabt's dangerous ball flew across the face.
Newcastle were offering little attacking menace, despite decent spells of possession, and QPR's resolute defender Ryan Nelsen easily dealt with any hopeful balls into the box.
Ba ballooned a free-kick hopelessly over the bar as the Magpies laboured on the increasingly sodden surface, but James Perch did raise the pulse of the home faithful with a shot narrowly wide.
Following a quiet first-half, R's striker Djibril Cisse nearly made his mark moments after the restart as Tim Krul pushed his low drive into the side-netting.
His namesake then went close at the other end as Papiss nodded over at the back post, while Vurnon Anita's dangerous low free-kick was pushed away by Rob Green.
The Magpies were mounting a sustained assault on goal, but substitute Ameobi made a mess of a header before Ba nodded weakly at Green.
Ameobi was far more assured shortly afterwards as he raced onto Perch's pass and curled an inch perfect shot into the far corner.
The R's back-line was almost breached again minutes later when a low drive from Sylvain Marveaux was pushed away by the sprawling Green.
Taarabt was handed the chance to give Rangers a last-gasp reprieve with a free-kick in a dangerous position, but his looping effort was held by Krul.