Osimhen rose highest to head home the winner with nine minutes remaining in Napoli's 1-0 victory at home to Torino on Monday (AEDT).
Napoli made it eight wins from eight games – the only team with a 100 per cent record in the top-five European leagues – to equal their best start to the Serie A season (after 2017-18), despite Lorenzo Insigne's missed penalty in the first half.
Osimhen revelled in his goal afterwards, with only Real Madrid's Karim Benzema (seven) and Borussia Dortmund sensation Erling Haaland (five) scoring more goals than the Nigerian forward (five) in September and October in the major five European leagues this year.
"It was the most important goal of my career," Osimhen said post-match. "I'm so pleased. The atmosphere at the stadium was incredible. The fans pushed us forward and we managed to get the three points.
"We never gave up, we attacked until the end and deserved the win. I saw the ball fly up and I thought I could get there before the defenders.
"I connected well and scored such an important goal for me and the team."
Napoli – who last won the Scudetto in 1989-90 – are two points clear of second-placed Milan.
"When you have strong players in attack, there are more solutions, so you always hope something can happen," Spalletti told DAZN.
"… I've seen an improvement in terms of mentality and compactness. Seeing [Matteo] Politano and Insigne track back is something that unites, gives strength and creates team spirit.
"We have a team of friends. We also want to propose a good football and tonight we were at a very good level. We built, fought and were willing to give what this game required."
"We obtained a big win for our fans who deserve it. We feel the passion for their love for these colours and the team. It was important to feel their joy tonight."
Insigne is the player who has missed the largest number of penalties (three) this season in the five major European leagues.
The Napoli captain missed his sixth penalty out of his 26 attempts in Serie A – considering only the current season, the Italian forward has scored two penalties out of his five attempts.
Since Napoli returned to Serie A in the 2007-08 season, they are the team that have missed the highest number of penalties in the five major European leagues (35).
"Lorenzo has a strong bond, especially with his team-mates who are helping him. He was sorry for not giving his contribution," Spalletti said. "For me, Insigne will take the next one, then it will be Lorenzo's turn and then the captain's."