Manchester City led at half-time after Castello Lukeba turned the ball into his own net, but Ridle Baku brought Leipzig level shortly after the interval when his cross found its way into the goal.
Enzo Fernández restored City's advantage with a superb header from Iliman Ndiaye's cross, only for Antonio Nusa to equalise again in a frantic second half.
Haaland eventually settled the contest, converting Elliot Anderson's excellent delivery after the midfielder had driven forward and created the decisive opportunity.
The Norwegian scored with just his 13th touch of the match, but Maresca insisted his striker's involvement must never be measured simply by how often he touches the ball.
"I said yesterday that it's always important that Erling is inside the game. We know that any moment he can help us and he can score goals," the City manager said.
"Tonight also we scored more goals with different players, so we created so many chances that unfortunately we missed. I'm very happy he scored. Happy for him. It's always a nice feeling to win and to be the captain."
Maresca agreed with Haaland's assessment that City still have plenty of room for improvement, particularly after conceding two avoidable goals.
"That we can do better? Absolutely, no doubt. That's why I'm so happy, so confident because I can see that we can do much better.
"For me it's a normal thing because it's just four months ago that we started. It's not automatic. You need time to work together."
The manager was particularly unhappy with the goals conceded.
"I think both Leipzig goals are quite silly goals that we can avoid. We are creating since day one, many chances in each games. But we need to avoid conceding silly goals."
He added that the players still needed time to understand his methods and each other, but was pleased to leave Germany with three points.
RB Leipzig coach Martín Demichelis was disappointed by the result but proud of his team's performance.
"If you lose, there's always a moment of sadness. You can't be happy. But there's different ways to lose, and the way the team played today, I'm just proud of my boys today. I think we deserved a point or probably more today. But that's football."
Demichelis also praised their competitiveness against one of the Premier League's leading sides, insisting the performance offered encouragement despite the defeat.
"It's a shame for the lads, for the fans, for the club. Three points from four games isn't enough. But this is the way, this is the right path, to fight, to play well at this level."