The Ligue 1 champions put themselves in a strong position to qualify for the last 16 with the victory, with goals from Juan Bernat and Neymar leaving PSG second in Group C with eight points from five matches.
Napoli currently lead the group with nine points while Liverpool sit third on six with those two set to face off in their final group stage match.
PSG, meanwhile, will face last-place Red Star Belgrade, knowing a win will see them through to the knockout stage.
Following an opening match loss to Liverpool, PSG appeared to be in a bit of trouble, but a 6-1 win over Red Star and two draws with Napoli helped vault the French side back towards qualification.
In the aftermath of Wednesday's victory, Al-Khelaifi says he is proud of his team's fight through the group stage and, in particular, the performance on Wednesday.
"Yes I'm very happy of the quality of our play," he told reporters.
"We showed our real face. Lots of people in the media were talking about our project and we showed the real face of the team. We're solid with a great coach. It's a great response for everybody.
"It was not easy, Liverpool is at a great level with some great players. Everybody has had a great match. Even the fans.
"For me Tuchel is the best coach in the world and he proved it today. We play every game to win the Champions League."
Thiago Silva also heaped praise on the manager, adding: "Our coach is amazing, it's a great answer for everyone."
Bernat opened the scoring for the French side, firing in the 13th minute following a deflection.
Neymar then doubled that lead in the 37th minute, becoming Brazil's all-time leading Champions League goalscorer in the process.
A James Milner penalty brought Liverpool back within one, but the Reds were never able to find that second goal as PSG held on to what turned out to be a vital Champions League win.
"We're very happy as we showed that we can rival with a team like Liverpool who has a great spirit. It was a great challenge," Tuchel said. "My players showed it. It's a great victory with a top display.
"You can't win without a great defense and team effort. We worked hard and the result is magnificent."
PSG return to league action against Bordeaux on Sunday as they look to maintain their 100 per cent record in Ligue 1 this season.