An impressive first-half display was rewarded in stoppage time, when Lemina drilled in a low shot following a corner.
Liverpool improved in the second half, with the returning Diogo Jota having a volley brilliantly saved by Alphonse Areola.
Substitute Sadio Mane’s looping header struck a post and Xherdan Shaqiri also shot narrowly wide but Fulham held on for their second Premier League win at Anfield.
A sixth consecutive home league defeat for Liverpool keeps them seventh on 43 points.
Fulham, unbeaten in eight away league matches, stay 18th but are now level with Brighton on 26 points, having played one match more.
Fulham midfielder Harrison Reed speaking to Sky Sports: “It’s massive. We came here with confidence. We knew if we could get something it would stand us in great stead. The manager breathed belief into us. He talked about coming here and winning. Not getting a point. Coming here and winning.
“The first half was superb, one of our best performances of the season. We knew they were going to come hard and we would have to dig in and put our bodies on the line and we did that.
“We did want it more and that was evident on the pitch and a big factor in getting three points today.
On momentum: “I think we feel that. We have been building. We have grown massively since the start of the season and I think everyone at home and in the league can see that as well.”
Also speaking to BBC Sport: “We are happy. We are struggling at the moment and it is hard to be at the bottom of the league but we still believe in our quality and we showed in the first half we can play against a big opponent and in the second half we showed good character. It is three good points for us.
“Honestly I am not going to lie, I was scared because they need to win some games. But I was so confident in my team. We have showed in all the games we have played that we play good football and deserve to be higher in the league.
“In the last game I missed a big, big chance and I wanted to say I can score. It’s a good goal because we win the game.
On what has changed: “I don’t know. We are just working so hard. I think we deserve better than this. We got the luck that we…..sorry I am losing my [train of thought] I am so tired.”
On staying up: “It depends on us and the way we play the other games. If we play like that I think we will stay up.”
on the managerial side, Fulham boss Scott Parker to Sky Sports: “The first half, we were what I wanted us to look like. I had full belief we could come here and get something.
“In the first half we had chances. The boys stuck to the plan and we were well worthy of the first goal. In the second half you don’t plan dynamics to go like that. We showed another side to us – character, resilience, dogedness. I’m very proud of the team today.
“Mario came up with a lovely strike. I’m very honest and I said to the players before the way we’re playing things will change. Today we were on the right side of that.
“There’s momentum with us as a team. It’s irrelevant who we’re bringing into it or the points difference until the end of the season. When the curtain comes down, we’ll work out whether we were good enough or not.
“I’m pleased for the lads. I’m pleased they got what they deserved. For large parts of this season, we’ve not managed to get what we deserve.”
Liverpool boss Jurgen Klopp react to the defeat in an interview with Sky Sports: “Fulham will cause us problems – it’s clear. They’re in a good moment, they’re a good team. We all agree a team like this should stay in the Premier League.
“There were moments we could have had more of an impact on the game. Conceding that goal before half-time was a massive blow. We tried to react and the boys showed that. In the end we don’t score goals and that’s a big problem.
“We never had a momentum in the season. You can see it’s still in the boys. They still have it all but at the moment can’t show it. It would be a masterpiece to find out how we change that overnight.
“[On suggestions Fulham players wanted it more] The winner is always right. My boys wanted it. It’s easy to judge they have won it so wanted it more. I don’t think that’s the problem.
“I don’t have to stand here and say we’re fighting for this or that.”