First this is completely dependant on what your contract says. If the contract says you will be paid for the actual hours worked then you get 10 minutes worth of pay for 10 minutes worth of work. If you claim that you worked 2 hours when you only worked 10 minutes in this scenario then you are committing fraud. I currently have a contract that states I will only be paid for work done onsite. In this case if I get a call and choose to remote in to fix the problem in 10 minutes so I do not have to drive into the office, then I do not get to bill anything. I am also not required to maintain any on call status or availability. If I get a call at 3am I can choose to ignore it.
You need to look at your situation. If you are required to have some availability off hours then you should negotiate some arrangement that will make sure that if your time off is interrupted you are sufficiently compensated. When I am required to maintain on call for support I try to negotiate a minimum 4 hour pay regardless of the problem. This prevents the calls for minor issues that can wait for the morning, or at least compensates you for dealing with them.
If it is going to be a regular thing that I am going to get a call to support after hours but not be required to be available, then you should have some sort of written agreement. This can even be an email from your supervisor saying you can bill 2 or 4 hours for any after hours call, and be paid for your drive time should you need to come in after hours.
If this is just an irregular thing (once every 6 months or so) and mostly about systems I support and most likely due to something I did I am not going to push the pay issue. This is the cost of doing business every once in a while you have to clean up a little mess. It is not good business to not be willing to give a little. While you may be entitled to the pay, and you should bill for the hours you work, asking for extra for the exception can be seen as greedy. In contracting you are your product so it is as important to make sure your brand is not tarnished by greed as it is to make sure that you are not seen as a sucker.