The 2014 champions crashed out in the group stage in the last two editions and Undav guaranteed qualification to the last 32 with his winner four minutes into stoppage time in Toronto on Saturday.
Captain Franck Kessie put the West Africans ahead on 30 minutes but Undav levelled off the bench in the 68th minute and also grabbed the last-gasp winner in the 94th.
"I try to bring my confidence on to the pitch, I know that I can score in every game," said Undav. "There are no nerves, it is just a football match."
A knee injury to centre back Nico Schlotterbeck forced him off at half-time in the only negative for the Germans.
Germany boss Julian Nagelsmann played the same starting XI who battered Curaçao 7-1 in their first Group E game.
The Ivorians dropped Elye Wahi to the bench from the team that started the 1-0 victory over Ecuador.
Aleksandar Pavlovi thought he had given the four-times champions the lead but he was penalised for jumping into the keeper, much to the annoyance of the German fans in the stands.
They were left to rue that just before the half-hour mark when Kessie netted after Amad Diallo's shot was blocked by Nathaniel Brown and it fell kindly for the scorer. At that point Ivory Coast were going through to the knock-outs early.
Fans of the Elephants danced for joy in the Toronto stadium extended for this tournament, just like the 48-team event itself. Third spot could also get the Ivorians through in the new format after their group finale against Curaçao.
The goal initially knocked the stuffing out of the Germans but they rallied when Havertz had the ball in the net, only for the referee to blow up for an earlier foul by Musiala.
It was clearly an Ivorian free-kick, but Germany queried why the official had waited so long to whistle.
Florian Wirtz then tried to walk the ball into the net when he should have pulled the trigger just before half-time.
Antonio Rüdiger came on for Schlotterbeck at the interval but Naglesmann resisted other changes until the 60th minute, despite Germany being too rushed and lacking a cool head.
Undav, who netted in the opener, was introduced alongside VfB Stuttgart team-mate Jamie Leweling and Mainz midfielder Nadiem Amiri.
It did not take long for Amiri's cross to be turned in from close range by Undav, who had feared he would not make the World Cup squad after negative comments from Nagelsmann.
Instead he is increasingly looking like Germany's talisman with his ninth goal in 11 internationals coming in injury time. Undav received the ball from Felix Nmecha and finished superbly on the turn.
"Deniz scored two top goals," Nagelsmann said. "He is the kind of striker who knows where the goal is."
But the coach stopped short of saying Undav should start going forward as his impact for the bench could be more important.
Ivory Coast will regret some misses and star Yan Diomande having a quiet game, while Wilfried Singo looked to suffer an injury.
