After becoming available on Outlook Mobile (see https://t.co/1LcJGaBI8j), you can now also instantly reply to an meeting request when you are using Outlook Web Access (aka Outlook on the Web).
Just select the meeting invite and you will immediately get the options to reply (Yes, Maybe, No, Propose another time with the possibility to add comment and reply (or not) to the organizer (aka send the response).