You definitely do need to sit down with your boss and discuss this issue before doing anything else.
If your boss is an experienced manager then your boss should have suggested that this is an issue to you and that you need to do something about it. Your boss could have also potentially offered you some advice on how to deal with the issue.
When you sit down with your boss you need to tell your boss that you are a very hands on manager, and you think that because your boss has responded to your subordinate directly, your boss is reducing your effectiveness to manage your team. The terminology used here is important, so I've highlighted the key bits in bold. You should also try and be as polite as possible, as the last thing you want to do is fall out with your boss.
As your boss has suggested all 3 of you sit down together, you should proceed to do so to avoid undermining your boss, but you need to make it clear to your boss prior to that happening that your boss is there to act as an observer, and that you expect your boss to back you up if the atmosphere becomes tense.
You should also ask your boss to avoid responding to future requests because you think that if your boss does, your effectiveness to manage your team is reduced. (It is import to repeat this point in a slightly different fashion so that it is very clear.)
When all three of you sit down together, your boss should give relatively little input, allowing you to direct the meeting. You need to be stern with your subordinate but not too stern so that it does not come across as if you are causing problems. You need to say that all requests should be coming through you first, because you need to be kept in the loop of what is going on, and by being bypassed, your subordinate is stopping you from being able to do your job effectively. Worse still, your subordinate could also be wasting the time of others by not doing so.
I would not go down the route of a Performance Improvement Plan if this does not work because it is quite drastic to jump straight into doing so. Instead, I would set up regular 1-2-1 meetings with your subordinate and keep relaying the same message, asking your subordinate if there are any particular reasons as to why your subordinate is not coming to you first.
At the end of the year I would have an annual performance review where you raise what has been happening as an issue and mention that the problems your subordinate is causing have been reflected in the review. You should mention that because of this your subordinate is less attractive to the company so has lost out on benefits others have been offered as a result, this should make your subordinate listen, as your subordinate will accept that you are the one in charge of your subordinate and not your boss, and by continuing to ignore you, your subordinate is the one losing out.
If after the annual review, there is still a problem, then I would consider putting together a Performance Improvement Plan. But as I said this is slightly more drastic and may draw attention to this problem more than you want.
I would also keep your boss in the loop, but make it clear that you are in control of what is happening. Explain your plan, saying you are happy to manage the issue by yourself at the moment, otherwise your boss may feel like you are not in control. Make it clear to your boss that you are happy to manage the issue by yourself, otherwise your boss may think you are asking for help and may try to get involved again.
Failing to get this right could see you becoming less and less relevant, so you need to nip this in the bud as soon as possible.