The Super Eagles broke the deadlock against the Panthers at the Moulay Hassan Stadium through Akor Adams after 78 minutes.
Mario Lemina found a late equaliser with his goal on 89 minutes to take the tie to extra-time.
Chidera Ejuke then gave Nigeria a 97th minute advantage and Victor Osimhen sealed the result with two late goals after 102 and 110 minutes.
Chelle said on Complete Sports after the game: "I am very proud of these guys because every time they are focused on what I ask, what I want, and it showed what I want.
"The word today was the passion, during my speech, it was about passion, it was about working together to have the same thing."
Nigeria next face Democratic Republic of Congo, who beat Cameroon 1-0 in their semi-final, for a place in the six-team intercontinental qualifier, which will be held in March.
"So they did it in today’s game, but we have a game in two days, and maybe after the game we can smile," Chelle added.
Nigeria head coach Eric Chelle sparked controversy after his team's World Cup Qualifiers Playoffs defeat, alleging that a Democratic Republic of Congo official performed "voodoo" rituals during the tense penalty shootout.
Victor Osimhen has emerged as the heartbeat of Nigeria's World Cup campaign, and all eyes will be on the Galatasaray striker when the Super Eagles take on the Democratic Republic of Congo on Sunday in Rabat.
Nigeria took a step towards World Cup qualification with an extra-time win over Gabon in their playoff semi-final as the Democratic Republic of Congo edged Cameroon.
Gabon head coach Thierry Mouyouma is happy to be the least favourite to progress in their FIFA World Cup play-off against Nigeria in Morocco on Thursday.
