City looked set for a disappointing start to the post-Pep Guardiola era after falling behind at the Etihad Stadium, but Marc Guehi equalised in the 84th minute before Josko Gvardiol completed a late turnaround with a stoppage-time winner.
The 2-1 victory gave Maresca three points in his first Premier League match in charge and offered an early glimpse of the resilience that defined much of Guardiola's successful spell at the club.
"It's the perfect day, to be honest. The perfect day," Maresca said.
"I was pleased at the end because we gave the fans the joy of the three points. I have to say that was quite emotional."
City dominated possession for long periods and finished with 13 shots to Bournemouth's five, but they struggled to turn their control into clear chances.
Erling Haaland endured a frustrating afternoon, including an early miss from Nico O'Reilly's cross, as Bournemouth held firm for much of the match.
City finally found a breakthrough when Guehi powered a header home from a corner with six minutes remaining.
The comeback was completed in the 91st minute when substitute Rayan Cherki slipped a clever pass through the Bournemouth defence. Gvardiol turned sharply before finishing, with VAR overturning an initial offside decision and sparking celebrations around the Etihad.
Maresca was particularly pleased with Cherki's impact after bringing the Frenchman on in the second half.
"The impact was unbelievable," he said. "He's that kind of player."
The City boss also joked about Cherki's reaction to being left out of the starting line-up.
"If he's sitting next to me and he's not happy, you all realise that he's not happy, because he's doing anything just to show everyone that he's unhappy," Maresca said.
Asked whether Cherki could start soon, Maresca replied: "Absolutely."
The Italian also stressed that City are still adapting, with several players only returning around 10 days ago after the World Cup.
"Unfortunately, we are still four, five players that for them, it's pre-season," Maresca said. "So it's a huge difference in terms of physicality. But we are going to be better and better."
Maresca also showed his willingness to experiment by using Guehi, normally a centre-back, in midfield.
"It's just in this moment, to find a solution," he explained. "I know Marc from Palace, and I always thought that he could be a good midfielder. Overall, it was a good performance from him."
The manager acknowledged that his squad is still taking shape as he searches for the right balance.
"Unfortunately, the squad is a work in progress," he said. "That's why I'm looking for new solutions, different things."
City may not yet resemble the dominant side that collected six Premier League titles under Guardiola, but their late comeback provided Maresca with an encouraging first step.
Manchester City's next Premier League match is against Crystal Palace at Selhurst Park on Friday.
