If it's the very last segment of your original ticket (don't do this for any intermediate sectors!) and if you have completely satisfied that there is no cheaper way to get yourself into business than buying a new, one-way ticket, then it should be OK.

Assuming you can check in online in advance and/or have enough time to obtain a new boarding pass for your final segment at the last transfer airport, I would just board with the business-class boarding pass, and effectively "no-show" for your original, economy-class ticket.

However - if you have luggage in transit, this would be a no-no. If you don't show up to take your final flight - in this case, meaning you don't have your economy class boarding pass scanned - then you will cause some issues (they could offload your luggage, unless they first ask onboard if you are on the plane, and you sort it out there).

If you have luggage, you really should discuss the issue with the gate agent before this flight.