The game began amid a tumultuous 24 hours in world football, with a group of 12 teams, including Liverpool, announcing plans on Sunday for a breakaway Super League and Leeds players wearing t-shirts in warmups that bore the Champions League logo and read: "Earn it. Football is for the fans."
On the field, Jurgen Klopp's team was looking to move back into the top four in the Premier League, starting the match three points behind fourth-placed West Ham United and two behind fifth-placed Chelsea, who also committed to the Super League plan on Sunday.
Mane netted for the visitors to Elland Road in the 31st minute -- ending a run of nine Premier League games without scoring -- when Trent Alexander-Arnold laid a ball off to the Senegal international to sweep home and stake his team to a half-time lead.
And the efforts of Marcelo Bielsa's team were not in vain, as Llorente headed in a deserved game-tying goal for Leeds in the 87th minute to put the brakes on a return to the top four for Liverpool.
Home-side striker Patrick Bamford joined a chorus of critics who condemned the drive by 12 of Europe's top clubs to form the breakaway competition rivalling UEFA's Champions League.
"We have just seen what everyone has seen," Bamford told Sky Sports. "It is amazing the things they are talking about. I can't comprehend. It is amazing the uproar and it is a shame it isn't like this with other things, like racism.
"We are like fans. We can't believe it and don't know what is going to happen. I haven't seen one fan who is happy, and football is ultimately about the fans. Without the fans football is nothing."
Liverpool midfielder James Milner added: "I can only say my view, I don't like it and hopefully it doesn't happen. I can imagine what has been said about it and I probably agree with a lot of it."
Bielsa praised his team for digging deep to avoid defeat after the match.
"There were periods when one dominated the other," Bielsa said. "Perhaps in the second half when we were losing we had more continuity when we were searching for the equaliser.
"We kept on being dangerous even though the opponent was defending close to their goal."
Bielsa's Liverpool counterpart Klopp put on a brave face after his team let victory slip away from their grasp.
"It is disappointing of course but we cannot say it was not deserved for Leeds," he said. "We had big chances in the first half but didn't use those.
"We will fight for the Champions League with all we have. This is a point more in the end. It is always best to win all the games but if not we have to shake a bit and go again and that is what we will do."
The result left Liverpool sixth on 53 points from 32 games, one behind fifth-placed Chelsea who have a game in hand and two adrift of West Ham in fourth. Leeds stayed 10th on 46 points.