A couple of far easier and non destructive method , since you are fortunate enough to have a grayscale pattern.
1) Create a NEW shape layer that covers the whole canvas.
2) In that layer go to Fx and make a gradient overlay to match the gradient in your desired image ( which seems like a basic linear gradient , so that should be a snap).
3) If it wasn't already, move the shape layer BELLOW the pattern layer
4) Set the pattern layer blending mode to multiply.
You can even have COLOR versions of your patterns by employing this method.
1) Copy your pattern into the clipboard.
2) Create a shape layer, covering the whole canvas, of the desired color.
3) Add a gradient mask to the shape layer
4) Option click ONCE on the gradient map ( the canvas should turn white) , and PASTE your pattern ; it is now pasted onto the layer mask you just made
5) Select ALL then , INVERT ( so that black turns to white and white to black)
6) Create a new shape layer
7) In that layer go to Fx and make a gradient overlay to match the gradient in your desired image.
Hope that helps