Slot’s side moved seven points clear of second-placed Arsenal thanks to Luis Diaz’s early opener and a Mohamed Salah penalty before the interval at Anfield.
It wasn’t easy for Liverpool despite that strong start as fourth-bottom Wolves hit back impressively.
Matheus Cunha’s blast reduced the deficit and Liverpool had to hold on in the closing stages before they could celebrate a first win in three games in all competitions.
Indebted to Alisson Becker for some crucial saves, Liverpool boss Slot said: "This one is big. We needed to fight and we needed Alisson.
"Wolves took a lot of risks. In a season where you want to achieve something, you need to have wins like this as well.
"It’s never the game-plan never to create anything at all. They got better and better, we got worse and worse.
"We had to show a different mentality and got it over the line. If this is what it takes to win a game then I’m happy the players could do that again."
Slot admitted Liverpool were running on fumes at times after Wednesday’s emotionally draining 2-2 draw at Merseyside rivals Everton, which featured a stoppage-time equaliser for the Toffees, and last weekend’s embarrassing FA Cup exit at second tier Plymouth.
"Fatigue comes from running a lot and a bit of mental fatigue a lot. We were mentally tested today. We thought we’d scored a third and then a penalty for the third but both were correct from the referee," he said.
"Maybe it did lead to us being a bit tired. I did see for the first time this season that players were more tired than they have been.
"If you want to achieve something it is not only about bringing the ball out from the back or Mo scoring goals, it is also about defending."
‘You can never breathe’
Liverpool’s ability to grind out a fourth win in their last five league matches kept Arsenal at bay in the title race.
Chasing a record-equalling 20th English title and their first since 2020, Liverpool are 13 games away from the trophy.
They face significant clashes with Aston Villa, Manchester City and Newcastle in their next three league games.
And Slot knows Arsenal - who have finished runners-up for the last two seasons - will do everything they can to take the race to a dramatic conclusion.
"If you look at the last few seasons it has mostly been a battle between two teams. As things stand now it mostly looks like between us and Arsenal," he said.
"You can never breathe in this competition. I saw Arsenal’s 15-game unbeaten run and the gap has always been the same so that shows that we do.
"If you want to compete for something special then you have to win a lot of games in this league."
Slot was able to sit on the bench against Wolves despite being charged with abusive behaviour towards the match officials after being sent off at the end of the stormy Merseyside derby.
The Dutchman could eventually face a suspension and he said: "It is an ongoing process, it is not smart to talk about it.
"We’ve seen the comments from the referee and now we can say our part. It’s down to a panel to decide if I get a ban."
Spurs edge Man United
Yesterday’s other game was between two teams unexpectedly struggling this season as Tottenham edged to a 1-0 win against Manchester United.
The result moves Spurs into 12th in the table while Ruben Amorim’s United remain in 15th place on 29 points.
On Saturday, Arsenal ignored their injury woes as Mikel Merino, sent on by manager Mikel Arteta to act as a makeshift striker in the closing stages, inspired a 2-0 win against Leicester.
It proved an inspired move as Merino netted twice in the last nine minutes to extend Arsenal’s unbeaten run in the league to 15 games.
Kai Havertz has been ruled out for the season with a hamstring injury, while Gabriel Jesus, Bukayo Saka and Gabriel Martinelli are al also injured, leaving Arteta with a threadbare attack.
Recent signing Omar Marmoush scored a 33-minute hat-trick for Manchester City at the Etihad Stadium to seal a comprehensive 4-0 win against Newcastle, with James McAtee’s 84th minute volley capping the win.
However, there was a scare for City when Norway striker Erling Haaland was forced off with a potential knee injury in the closing stages.
Third-placed Nottingham Forest slumped to a 2-1 defeat Fulham, while Bournemouth are up to fifth as their unlikely bid to qualify for the Champions League gathered pace with a 3-1 win at bottom of the table Southampton.
Ten-man Ipswich held on for a 1-1 draw at Aston Villa after defender Axel Tuanzebe was sent off just before half-time. Liam Delap put Ipswich ahead before Ollie Watkins tapped in the equaliser after Marcus Rashford’s free-kick hit the bar in the 69th minute.
Elsewhere, Kevin Schade’s fourth-minute goal clinched Brentford’s 1-0 win at West Ham.