It finished level at the Vitality Stadium as the visitors impressed greatly on their Premier League promotion.
The Blades made a bright start in the first half and saw McGoldrick’s strike saved early on, before Robinson had his long-range effort parried wide.
After the interval, the hosts went ahead against the run of play when Mepham bundled home following a goalmouth scramble.
However, Sheffield got a deserved equaliser late on as Sharp reacted quick to a loose ball in the box before firing beyond Ramsdale.
Eddie Howe’s side travel to Aston Villa next weekend, while Sheffield United welcome Crystal Palace to Bramall Lane on Sunday.