That was what this game was about and why it was so crucial to both managers.
It was a game both Tuchel and Klopp simply dared not lose – particularly after wins for Everton and Tottenham earlier in the night.
Defeat for Chelsea would have seen them leapfrogged by Liverpool ahead of the visit of Everton to Stamford Bridge on Monday.
In truth that never looked likely in what was Chelsea’s most complete performance under their new manager.
Mason Mount’s first half strike was enough to secure the points – but victory could have been far more emphatic, even if they were fortunate not to concede a second half penalty when N’Golo Kante handled in the area.
Timo Werner – for so long a Liverpool target – was outstanding.
He found the back of the net in the first half, but saw his goal ruled out by VAR for a debatable offside.
It was a performance that brought to mind the German’s form from his RB Leipzig days as he played on the shoulders of Liverpool’s centre-backs, and was twice fractions away from making a decisive connection from close range.
Hakim Ziyech also saw a shot cleared off the line by Andy Robertson.
But it was Mount who provided the key moment, cutting in from the left in the 42nd minute and sweeping a low shot into the corner past the dive of Allison.
On the face of it a 1-0 win might sound like business as usual for a Tuchel team that has been mean at the back and blunt up front.
But that was not the case, despite his pre-match assertion that there would be few thrills.
This was a complete performance from his side – full of attacking intent and resolute at the back as Liverpool pushed for an equaliser.
It wasn’t until Gini Wijnaldum’s late header that Edouard Mendy had a save to make.
Andreas Christensen was imperious in the centre of defence, while Cesar Azpilicueta and Antonio Rudiger put up road blocks either side of him.
Victory moves Chelsea up to fourth and capitalises on more dropped points from Manchester United and Leicester this week.
Another win against Everton and they may start to think about more than just fourth place.
Gareth Southgate has embarrassment of riches when it comes to attacking midfielders – but Mount is surely a guaranteed starter.
While it will be difficult to leave out the likes of Jack Grealish, Phil Foden and James Maddison, if fit, he has to pick a team that gels.
Mount is the type of player who does precisely that. He makes other players look better.
He’s absolutely key to this Chelsea team and midfield partnership with Phil Foden would be up there with anything any of England’s Euro 2020 rivals could field.
Grealish and Maddison are hardly bad game-changers to bring off the bench.
When is a handball not a handball? The answer to that appears to be whenever a Chelsea hand is involved.
Callum Hudson-Odoi was lucky to avoid conceding a penalty against Manchester United on Sunday – and on this occasion it was N’Golo Kante who palmed the ball away in the area without punishment.
While Chelsea could feel aggrieved after seeing Werner’s first half strike ruled out by VAR for a marginal offside – they were definitely on the right side of a controversial call when Liverpool’s players were convinced they would be awarded a spot kick.