The OED clearly recognises the word difficultly, though it can imply different things.
The senses are:
1 a. Not easily or readily; with difficulty. 2014 D. Renee Cinderella Not xi. 56, I told myself it was going to be okay and very difficultly tried to calm myself.
1 b. So as to be difficult to understand; in a complex manner; obscurely. Now somewhat rare. 1988 Sunday Tel. 9 Oct. 20/8 Mr Vansittart's difficultly intricate but richly rewarding mythological novel.
1c. So as to be difficult to deal with. 2010 Dunoon Observer & Argyllshire Standard 25 June 23/1 The course was playing as difficultly as it had been for the previous week's Argyll and Bute team trophy.
1d. So as to be in an awkward or delicate position or situation. 2014 Frontier Post (Nexis) 9 July By every indication they are far more difficultly placed in Afghanistan.
- Unwillingly, reluctantly. Obs.1683 J. Nalson Present Interest Eng. 44 Which they now difficultly acknowledge, it is easie to foresee.
Clearly it is not 2. And I don't see much difference between 1b and 1d. But for your example there would be nothing wrong with your using the 1a sense and saying "Difficultly, they won". But it would be rather unusual. The more current way of saying it would be "With difficulty, they won."