Chris Mepham's first Premier League goal, when he smashed in a rebound after Callum Wilson's shot on the turn had been parried by away goalkeeper Dean Henderson, had looked like giving Bournemouth the three points.
Sharp, 33, had only played in two Premier League matches before - both at the start of the 2012-13 season while at Southampton - and began on the bench, despite being the Blades' top goalscorer with 24 goals in all competitions in 2018-19.
"I wanted to get on the pitch and help the football club out," said Sharp. "We put bodies in the box, managed to create something and I was the lucky one to get on the end of it.
"It was what I dreamed of last night and it was a proud moment for me and the family.
"I'm very proud of the boys, they were magnificent. It's a great point, we're off the mark and deserved something out of the game."
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