Why does manifold pressure increase with power? Whilst writing an answer to this question, I remembered something I don't really understand.

The partial vacuum in the inlet manifold is caused by the piston descending with the inlet valve open during the "suck" phase of the Otto cycle.  It is this vacuum that causes fuel to be pushed into the intake, the greater the vacuum, the greater the fuel added to the inlet charge and the greater the power.

Since the needle valve is on the manifold side of the throttle butterfly along with the input to the MAP gauge, why does the manifold pressure increase with power?  I would have thought more power, more "suck", lower pressure; more pressure, less "suck", less fuel.  

I'm obviously wrong since that's not how it works but why?

The answers to this question get close but I'm still missing something (and I'm sure will soon be embarrassed by the obviousness of the answer).
Manifold pressure is actually a measure of the vacuum pressure between the throttle and the cylinders. The more the throttle is opened, the closer that manifold pressure returns to atmospheric pressure.  

The amount of fuel provided to the engine depends on the pressure difference between the manifold and the throttle body.  The throttle body pressure will decrease as the throttle is increased, because of greater rate airflow across the venturi (faster air -> lower pressure).  The manifold pressure will increase as throttle is increased, due to the greater flow of fuel/air mix into the manifold (greater mass of air flowing into a fixed volume -> higher pressure).  So the pressure difference will get larger as the throttle is increased.  

This link has a pretty good description of what's going on.