How to cope with urgent request at a time when the correct authority is absent and unable to give approval.?

First of all , its usual to encounter such a situation. Mostly,in Purchase dept. there would be other designated people to deal in absence of other. If such a system is absent, Purchase dept. will be under the authority of project manager. or deputy Project manager, so he has got the authority to give the signature. requirement of such purchase can be checked by anyone related to it. 

I think this could help you to drive through your question. Correct me If I am wrong. Thank You.