Anderson delivered an energetic midfield performance at the Red Bull Arena on Wednesday, finishing the night with 102 touches, 10 ground duels won, seven tackles and seven recoveries.
His contribution was capped by a decisive assist for Haaland, who scored the winner with a determined run and precise cross from the summer signing.
Manchester City had taken the lead through a Castello Lukeba own goal and went into half-time ahead. RB Leipzig equalised shortly after the break when Ridle Baku's cross found its way into the net, but Enzo Fernández restored the visitors' advantage with a header from Iliman Ndiaye's delivery.
Antonio Nusa levelled again for the hosts before Haaland settled a five-goal contest, finishing Anderson's cross to secure all three points.
The Norwegian was quick to acknowledge the midfielder's impact since arriving at the club.
"He's been amazing," Haaland said. "He's had an amazing start to his City career and that's what you expect, you have to come straight in and perform.
"That's how the world is now and it's not easy, normally you need time to adapt and time to get to know your new teammates and the new coach.
"He's been impressive. Respect."
Anderson's ability to influence the game in and out of possession was reflected in his statistics, but Haaland's own contribution was rather more economical.
The striker scored with his 13th touch of the match, continuing his impressive record against Leipzig. The goal was his 13th in nine career appearances against the German club, making them the opposition he has scored against most often.
"13 touches, it's not the most but what is the most important? I helped the team to win so I'm super happy," Haaland said.
The forward was nevertheless keen to stress that City could have managed the contest better after taking the lead.
"In the end we need to step up a little bit. When we were 1-0 up we needed to push forward a bit more to go for the second and third. We have to work on that."
Haaland acknowledged the difficulty of maintaining concentration throughout a demanding European fixture, but said he preferred to view the challenge positively.
"You can look at it in a few different ways. You can look at it as it's difficult to keep concentrated for 100 minutes or look at it in a positive way that it's only 100 minutes to be fully focused to hopefully be ready when the chance comes.
"I look at it in the second option."
The victory provided another reminder of Anderson's growing importance to City, with Haaland particularly impressed by how quickly the midfielder has adapted to his new surroundings.