You don't need a stencil buffer. I don't think more triangles will help, either — more likely that'd just cause you more confusion because you'd be assigning per-vertex colors to intermediate vertices and having to interpolate them yourself.
Your gradients are coming out that way because of how and where you assign vertex colors for interpolation. Notice the difference in colors between your output and the example of what you're looking for:
You've got 100% red at every vertex along the top edge of your graph, and 100% green at every vertex along the bottom edge. OpenGL interpolates colors linearly across the face of each triangle, which is why you've got more red in the shorter parts of your graph.
In the output you're looking for, the top of the graph starts out less red in the shorter parts, so that it makes a shorter transition to white in over shorter distance.
There are a few different ways to do this, but probably the easiest (for your plan of using GLKBaseEffect instead of writing your own shaders) might be to use a 1D texture for your gradient, and assign a texture coordinate to each vertex that's proportional to its Y coordinate on the graph, like so:

(The example coordinates in my diagram assume your graph vertices cover the range 0.0 to 1.0, but the point stands regardless: the vertical texture coordinate for each point should be a fraction of the graph's total height, between 0.0 and 1.0.)
Alternatively, you could look into drawing in two passes: First, draw the shape of your graph, then draw a quad (two triangles) covering the entire screen with your gradient, using the appropriate glBlendFunc so that it only draws over the area you've filled in with your graph shape.