Use a guide bar for pouring.
I learned how to do this kind of thing in a lab using a glass rod and a cylindrical container. A similar technique can be used for your household situation.
Find a spoon or some round handle utensel that can span the diameter of the sauce pan.
Gently, tip the sauce pan using the handle of the spoon where it touches the pan edge. The liquid will tend to cling to the contact point.
Here's a small version of what you'll be doing:
Put your container under this 'spout' and you shouldn't lose more than a couple of drops.
Practice makes perfect.
You'll get the best result if the rod is held nearly vertical as you tip the sauce pan while maintaining contact between the rod and the edge of the sauce pan. Some would use the back of a narrow spoon to get the same result. A chopstick would be another possibility.
While the pan is very full, if you tip it only slightly, you'll find that the liquid pours over the rim of the pan and then instead of pouring away from the pan it will run down the side of the pan until it reaches the point where the side meets he bottom, whereupon it will run off the pan in a single stream. Positioning your cup at the bottom of this stream will mean you can pour down the side of the pan and into the cup
I use this effect (Coanda effect) to empty a full pan to a point where the pan can be more quickly tipped up to a steeper angle that will ensure that the liquid in the pan ejects from it rather than tending to stream down the pan side - in essence when making, for example, 4 cups of cocoa the first one or two cups will be filled by pouring down the side of the pan and the remaining two filled by pouring normally as one would expect
With practise you'll get to know when you're approaching the point where the liquid will break away from running down the side of the pan and become a poured free falling stream so you can switch tactic (normally by bringing the rim of the cup into contact with the side of the pan and tipping the pan up quickly into a pouring position)