After Southgate's confidence in center-back Harry Maguire backfired in both goals, the knives were being sharpened for him.
Gundogan scored the game's first goal from the spot after Maguire gave the ball to Jamal Musiala before chopping down the Bayern Munich midfielder. Maguire has been publicly backed by the England manager despite being benched by Manchester United manager Erik ten Hag at the club level.
Then, after Maguire was eliminated in the German half, Havertz curled superbly into the top corner.
However, two goals in three minutes changed the atmosphere at Wembley and increased questions about Southgate's future before the encounter in Qatar. These goals were England's first from open play in 512 competitive games.
Despite not having played much for United, Luke Shaw was reinstated to the starting lineup and launched the comeback by volleying in at the back post.
Later, two of Southgate's subs worked together lethally as Bukayo Saka set up Mason Mount to score a curling goal.
Following a VAR review for Nico Schlotterbeck's foul on Jude Bellingham, Harry Kane's penalty in the 83rd minute seemed to have given Southgate's team a spirit-boosting victory.
However, Germany, a four-time world champion team that was also having a rough time heading into Qatar, managed to salvage a point when Nick Pope fumbled Serge Gnabry's attempt and Havertz pounced on the rebound in the 87th minute.
Late in the game, substitute Bukayo Saka nearly gave England the victory as the crowd pondered why it had taken the hosts so long to allow any kind of free play.
With three points less than Germany, Hungary, and Italy, who finished first in the group and advanced to the Nations League final four, England came in last place in the group.
The previous time England lost six consecutive competitive games was more than a century ago, but their inspiring comeback victory over Germany at least altered the narrative.
The recent results have put the boys under pressure, and we all came to this game with something to prove, Kane stated. We still have things to learn from the mistakes we made, but we scored three goals, and I think that will help us have a good attitude going into the World Cup.
Both teams needed a pre-World Cup pick-me-up following disappointing Nations League campaigns, with Germany losing to Hungary at home by the same score last Friday while England was demoted after losing 1-0 to Italy on the road last Friday.
The two heavyweights last faced off at Wembley during the Euro 2020 championships, with England coming out on top 2-0 and riding a high. The lone goal they had scored in their previous five Nations League games came from Kane's late penalty in Germany, which contributed to the mood's gloom.
