If photons have no mass, how will a black hole drag in light?

Your question implies a knowledge of Newton's model of gravity, but lacks a knowledge of Einstein's model of general relativity.

The black hole warps the "fabric" of space time, so much, that the light follows the curvature of space and falls in.

Good question :)

It has nothing to do with light's mass or a black hole 'dragging light in'.

Light just follows the curvature of space created by the immense gravity of a black hole.

Black holes kinda warp the geometry of space.

Light goes in a "straight" line. All gravity bends space so that light actually curves around a little. Near a black hole space gets so far curved that the light going in a "straight" line can actually orbit the black hole or turn all the way in.

The immense gravitational field of a black hole warps the space around it, and light follows the shape of space - right into the black hole if it passes close enough.

Black Holes drag in anything and everything.