Nathan Hughes scored the only goal of the game in front of a crowd of almost 4,250 at Hereford's Edgar Street ground.
The club was formed in the wake of the collapse of Hereford United, which was wound up in December 2014.
Chairman Jon Hale said there was a "lot of love" for the "phoenix club" in Hereford.
The goal came midway through the second half.
Nathan Hughes will write his name in Hereford FC history as the player who scored the first goal at the new ground.
The new club has negotiated a five-year tenancy at Edgar Street - the former Hereford United ground.
Mr Hale said the match against FC United - which was founded by Manchester United fans in response to the Glazer family's takeover - was particularly special because Hereford had drawn on that club's experience.
FC United have risen through the non-league ranks over the past decade and will start the new season in The National League North - previously the Conference North - after promotion from the Northern League.
"They have had a fantastic journey and have been really helpful and given us lots of advice," Mr Hale said.
Hereford United was wound up by a High Court judge after a petition brought by HM Revenue and Customs, which is thought to be owed Â£116,000.
The club was expelled from the Football Conference in June 2014 after failing to pay creditors.
Hereford FC will play in the Midland Football League. Their league season will begin on 8 August.
So-called "phoenix football club" Hereford FC have won their first home match against FC United of Manchester.