Its definitely not common to find, my apartment was sheer luck: It was going to be ~$5k, but the landlord got sued for violating rent-control, and was required to re-rent it at the "historic" price, so sheer luck on my part.
Most places will be rent-controlled, if they're older buildings (so your master-bedroom situation is probably rent controlled). If the landlord can't provide an exemption certificate from the city, you can assume its rent controlled (you can also ask the city to provide the status for an address).
The best way to find under-market places are to look for for-rent signs and craigslist. Think anything cheap and easy. Again, this landlord isn't making money and doesn't want to spend money. Anecdotally, avoid anything that has changed hands recently, because that landlord just bought the property to profit (and probably has an active loan to pay off). My landlord thought he could buy a property, evict poor residents (illegally) and jack up rent - and its sheer luck someone caught it. It is explicitly illegal to evict a rent-controlled tenant with the intent of increasing rent.
Rent control doesn't determine price once it hits the open market (with some exceptions), but it limits price increases and limits the ability of the landlord to evict you to find a higher-paying tenant. This incentives staying where you are once you find a good-enough place instead of moving around a lot - the goal is to provide a way to keep long-time residents as alternative to home ownership.