I think you can do it with a Service PO if you know the cost centre (account assignment) and cost element. God to ME21N and select Standard PO type, but in the Item Category select D for services, in Account Assignment Cat, select K for cost centre.
You do not need a service master record, just type in your short text and quantity and price.
Maintain the Account Assignments (CC/CE or GL) and get approval of PO (release), if required.
once PO released, you can do ML81N service entry sheet, accept it and save.
An automatic GR number will be saved as non-stock GR.
Quote this GR number for FI team to create internal invoice and pay.
Hope this will help.