Sharp's son Luey was just two days old when he died on Saturday, with the striker missing the Championship game with Coventry City at the Keepmoat.
He made a surprise return against Middlesbrough on Tuesday night, and - after a minute's applause in memory of Louis - scored a stunning volley to put Rovers ahead after 14 minutes.
He celebrated by showing a shirt dedicating the goal to his son, with referee Darren Deadman discarding the rulebook and not booking the forward.
"I knew what was going on all week and I also know the finer details of what happened, which is worse than you think," said Doncaster boss Saunders.
"He rung me last night [Tuesday] and asked me if he could play - he wanted to play. He wanted to play to score a goal for his son and his family and he was ready to go.
"When he said that to me I couldn't really refuse. You won't score a better goal than that - it's incredible. I thought 'the story's already been written. He's going to end up with a hat-trick here and we're going to win 3-0'.
"It didn't turn out that way but I'm really proud that he wanted to play and it tells you a bit about him as a man. There's not many people who would have done that."
Although Boro went on to win 3-1 and leave Rovers bottom of the table, the result was overshadowed by the death of Louis.
Sharp joined the Iron from Sheffield United in the summer of 2005, scoring 56 competitive goals before returning to the Blades two years later.
After once again failing to establish himself as a regular at his boyhood club, he joined Rovers in September 2009 - initially on loan, before making the mover permanent in a £1.1million deal.