According to Astronautix, Leonov's Berkut space suit had an open cycle environmental system with a relief valve, and he simply set the valve to a lower pressure setting:
Oxygen, used for both breathing and cooling, was contained in a metal backpack. A relief valve vented the suit into space, carrying away heat, moisture, exhaled carbon dioxide, and unconsumed oxygen. There were two relief valve pressure settings - 0.27 atmosphere or 0.40 atmosphere. Sufficient oxygen was carried for 45 minutes of depressurized activity. It was only worn on the Voskhod 2 flight, when Leonov had great difficulties in getting back into the airlock due to the suit's stiffness. It was only after switching to the lower relief valve pressure setting that, bathed in sweat, he was able to get the hatch of the inflatable airlock closed.
According to the Wikipedia article on the Sokol pressure suit -- the successor to the Berkut, sharing the same open cycle system and same relief valve pressures -- the low pressure setting is intended only for "extreme emergencies".