What you describe is a technique called averted vision and takes advantage of the arrangement of cones and rods, two types of light sensitive elements within the eye:
The retina contains two types of photoreceptors, rods and cones. The
rods are more numerous, some 120 million, and are more sensitive than
the cones. However, they are not sensitive to color. The 6 to 7
million cones provide the eye's color sensitivity and they are much
more concentrated in the central yellow spot known as the macula. In
the center of that region is the " fovea centralis ", a 0.3 mm
diameter rod-free area with very thin, densely packed cones.
Shorter, the cones are sensitive to color and work best in bright light, while the rods are most effective in low light conditions. And since the rods are concentrated off center of retina, our night vision is best off center. This averted vision technique can be used with a naked eye, as well as with any optical equipment like binoculars or telescopes, although it can be a bit of a bother with eyeglasses and contact lenses. Especially with the latter, using this advert vision technique can cause additional irritation of the cornea.
As per "beating the system" part, with a bit of practice, you could train yourself to view dim objects better with the corner of your eyes at will, and not merely by chance or for only short periods of time. It might seem hard with first few tries, but it really isn't and you soon get used to not looking directly towards the observed object, countering what we tend to do naturally, direct our eyes towards the object of our observations. Practice makes perfect, but there is no long term and unwanted side effects to doing this, and you'll still be able to direct your eyes towards whatever you'll want to see clearer, just as you did before.
There is one other thing to add to techniques to observing the night skies. Namely, our eyes need some time to adapt to darkness, and with our more frequent staring in computer monitors, television and other illuminated sources, our pupils need even longer to dilate and let the maximum of light to fall on the retina. So for best results, rest your eyes and do not expose them to anything except red light for 30 minutes prior to observing. This allows your pupils to expand to their maximum diameter and build up the levels of optical pigments, which are rapidly lost if exposed to bright light.
It is also important to observe with both of your eyes open to avoid fatigue. If you find this difficult, you may try covering the other eye with your hand or an eye patch. It should also be mentioned that both smoking and drinking cause deterioration in your sight. Your blood-sugar levels are also important and a low level of blood sugar causes lowering of sensitivity of eyes.
Lastly, your eyes will tire using this technique, just as they would by focusing for longer periods of times as you normally would. Look away every now and then, preferably not towards too strong sources of light, but still at least slightly brighter than those you previously observed. Also stretch your legs and blink fast a few times. Stretch your back too, and relax your bottom. You might find it funny, but this technique of relaxing and contracting muscles of that part of our physique has been used by trained spies to cheat polygraph tests that also measure pupil dilation. How's that for "beating the system", huh? It is by far the fastest way of relaxing your eyes, at least that I know of.