The 57-year-old was found dead on Wednesday in a lake near the family home in Southern Brazil.
Liverpool had not won their last four Premier League games prior to their visit to the Bramall Lane.
And after failing to break the deadlock in the first half, Jones put the Premier League champions ahead three minutes after the break.
The visitors doubled their advantage midway through the game when Brazil striker Roberto Firmino's shot was then deflected home by Kean Bryan, with the Blades defender eventually credited with the own goal.
Speaking to the media after the game, Jones who scored his first Premier League goal for the Reds, dedicated the win to Alisson’s dad and family.
"It’s been a difficult time for me and the rest of the team,” the 20-year-old told the media after the game.
"This goal is for Ally’s dad. If he sees this, this is for you bro.
"He’s a strong lad and a big part of the team. We miss him for sure. I’m dedicating my goal to him and his dad, and his family.
"It was a good team performance. I’m happy that we get the points and we can go again.
"It was a good example of putting it all together. I am happy I score and I’m happy for the rest of the team."
