Having taken 13 points from their opening five fixtures in Group C, the Three Lions simply had to avoid defeat against the Azzurri to confirm a top-two finish in the five-team section.
England had already avenged their Euro 2020 final beating against Italy with a 2-1 win in Naples back in March, but a full-strength side were left shell-shocked by ex-West Ham United striker Gianluca Scamacca just 15 minutes in.
Southgate's men - who had been on top in the early exchanges - were made to pay for lackadaisical defending, as Scamacca was left alone inside the box to fire home from Giovanni Di Lorenzo's cutback.
Gianluigi Donnarumma received adequate protection in the Italy goal, but just 17 minutes after falling behind, England were awarded a penalty as Di Lorenzo scythed down a charging Jude Bellingham inside the box.
Harry Kane was made to wait for his 60th England goal due to a lengthy VAR check, but the Bayern Munich attacker calmly sent Donnarumma the wrong way to draw his side level heading into half time.
After playing a key part in the Three Lions' equaliser, Bellingham produced a sublime piece of individual skill to set England away on the counter in the 57th minute, and the 20-year-old proceeded to lay off Marcus Rashford, who cut inside and unleashed a rocket into the bottom corner.
England's slender advantage was never really threatened by the Azzurri, and Southgate's men punched their ticket to Germany 13 minutes before the end thanks to Kane's record-breaking 24th Wembley goal for the Three Lions.
Speaking to Channel 4 after his side's triumph, Southgate insisted that there is more to come from his team and believes that the Three Lions were dealt the most difficult group-stage draw against the reigning champions, Ukraine, North Macedonia and Malta.
"We're so hungry, so eager to learn, so together. And you saw that in the performance tonight. We said before that mentality was the main thing. The performance was relentless tonight," Southgate said.
"There were times in the first half we were passive near our own goal. The biggest difference in the last couple of years is that we have more legs and physicality in midfield. You need to be outstanding without the ball against world-class teams.
"We need to make sure we are one of the top seeds next month. We need to win our next two games. We want to be in control of that. We need to keep building. There is more to come from this team. This was the toughest qualifying group, with the seedings. People have criticised us for not beating the top teams enough. But we have performed really well."
Southgate unsurprisingly reserved special praise for Real Madrid hotshot Bellingham, who wowed the Wembley crowd with another scintillating display on the back of registering 10 goals in his first 10 games for his new club.
"His mentality is incredible. To show such maturity and humility at such a young age is incredible and we're lucky to have him," Southgate added. "I think he's been a catalyst. I just think the way he carries himself and the way he plays on the field shows that. He has had that since he walked through the door frankly.
"Plus, the power in his play, that gives us something when you're in tight situations and he can wriggle out of things. But I think that belief, that willingness to engage with the crowd, they are rare traits in a player so young."
With 16 points from six matches in Group C, England are also guaranteed to finish top of the section, as Ukraine - who are three points behind - cannot catch the Three Lions due to their inferior head-to-head record.
England still have two dead rubbers in Group C to come next month, hosting basement side Malta at Wembley on November 17, three days before a trip to North Macedonia in their final qualifying encounter.