VAR frustrates Emery as Villa miss chance to top Premier League
The visitors kicked off bottom of the table, with Birmingham club Villa having won their last 15 home games in the Premier League.
But Cameron Archer, sold by Villa to the Blades in pre-season, stunned the home fans at Villa Park by opening the scoring in the 87th minute with a close-range shot.
Substitute Zaniolo rescued a point for Villa with a header seven minutes into stoppage time.
Villa needed a win to go top of the Premier League for the first time since August 2011, having not led the table at this stage of the season for 25 years.
But they remained behind leaders Arsenal on goal difference despite dominating possession and having the better of the game's chances.
Leon Bailey had the ball in the net early in the second half but it was ruled out by the video assistant referee, with VAR also rejecting three Villa penalty claims.
"I am very happy and very proud of the players," Emery told the BBC.
"It was very difficult to keep our winning record. They defended really well."
He added: "I accept VAR always. But only today I think it was too much. It was not necessary to review two or three times in the first half. And the goal, it was not necessary. Normally we can accept this goal.
"We are disappointed with the result today but we are accepting it. We have to focus for the next match against Manchester United, it will be incredible."
Sheffield United manager Chris Wilder said: "Being greedy, and the manner of their goal as well, (I wanted three points) but we'd have definitely have settled for a point before the game.
He added: "There's plenty to work with with the players and this result gives me great hope."
Villa's first brush with replay rejection Friday came when Ollie Watkins was shoved by Vini Souza, with another penalty appeal turned down by VAR when George Baldock blocked Watkins' header from the ensuing corner.
Villa thought they had gone ahead in the 58th minute when Watkins intercepted as United tried to clear a corner and exchanged passes with Jacob Ramsey.
The England striker then crossed for Bailey to sweep in but the goal was disallowed when Ramsey was ruled to have fouled Blades goalkeeper Wes Foderingham at the corner.
Another VAR reprieve for the visitors came 15 minutes later when Baldock came through a handball review.
United struck three minutes from the end of normal time.
Vini Souza's free-kick found Gustavo Hamer and the midfielder's fine piece of skill took John McGinn out of the game.
The substitute then cut the ball back for Archer to convert from six yards.
Foderingham saved Alex Moreno's header but Villa equalised in stoppage time when Zaniolo headed in Douglas Luiz's cross.
