The home team looked well in control but a late goal by David Clarkson led to an anxious few final minutes for Rangers.
Davis' strike was his first SPL goal and this win keeps Rangers clear at the top of the table.
The home side squandered an early chance when Kenny Miller shot over from the edge of the box when he should maybe have passed to the unmarked DaMarcus Beasley.
Stephen Craigan was deservedly booked for pulling down Miller, but Rangers were finding it difficult to create chances.
Miller turned well but his curling shot was brilliantly touched behind by Graeme Smith.
Just before half-time, Kris Boyd played a superb pass through to Miller but the striker's shot under pressure rolled just wide.
Neil Alexander made a brave save at the feet of Clarkson at the start of the second half before Beasley's powerful strike tested Smith.
The home team finally made the breakthrough when Miller's touch found Davis, who controlled the ball well before shooting powerfully past Smith.
Motherwell responded strongly to this set-back and Steven Hammell's shot from 20 yards went close.
Clarkson then brought a great save from Alexander with his curling shot which was going inside the far post.
Rangers looked to have settled the game when Smith could only palm out Miller's cross which hit Novo and rolled over the line.
Motherwell never gave up and substitute Jamie Murphy cut past Kirk Broadfoot before finding Chris Porter, whose mis-hit shot spun off the post to safety.
The visitors pulled one back when Porter's cross was bundled home by Clarkson, but Rangers managed to run down the clock to earn all three points.