I suppose it's grammatically correct and it would work in some contexts. I used to play chess for a club and it was always beat and never win against. Manchester City beat Southampton 2-0. Ireland beat Wales in the Six Nations. He beat all the opposition.
This is only a suggestion, but perhaps win against refers (or tends to refer) to the nature of the opposition rather than to the person or the team you beat. We were in League Two and Arsenal were in the Premiership, so it was always going to be difficult to win against such odds.