The Three Lions boss travelled to Qatar aiming to go one better at a major tournament once again, having led England to the semi-finals of the 2018 World Cup before collecting a runners-up medal at Euro 2020.
England began their quest for glory in the Middle East in ideal fashion, with five different players scoring in an eight-goal thrashing of Iran at the Khalifa International Stadium.
Bukayo Saka scored twice alongside strikes from Jude Bellingham, Raheem Sterling, Marcus Rashford and Jack Grealish, with Mehdi Taremi responding twice for Team Melli.
By leading England to victory on Monday lunchtime, Southgate has now recorded nine major tournament wins as a manager - the most in the history of England's men's team.
Ramsey - who famously engineered England's run to the 1966 World Cup trophy - was the previous record holder in that category with eight wins, but Southgate has now written himself into the history books.
Despite a lengthy delay due to Iran goalkeeper's Alireza Beiranvand's head injury, England quickly rediscovered their stride as Saka, Bellingham and Sterling all scored before the end of the first half.
Saka's second of the game put England 4-0 up before Taremi's quick response, and the goals would seemingly cease after Rashford and Grealish came off the bench to score late on.
However, in the 10th minute of second-half stoppage time, Taremi struck his second of the day from the penalty spot after John Stones had pulled down Morteza Pouraliganji, which left Southgate a "miserable so-and-so" at the end.
Speaking to BBC Sport after Monday's win, Southgate said: "[I'm] a bit fed up with the end of it really! To win by that margin and play as we did, you've got to be really happy.
""It was a sticky first half, lots of stoppages but we were a real threat throughout - our pressing was really good, our movement was really good.
"I've got to be really happy but we shouldn't be conceding two goals at that stage of the match and we'll have to be right on our game against the [United] States.
"To win by that margin - to play as we did for the majority of the game - we've got to be really happy. That's a great marker to put down. It's a great start but we're going to have to be better.
"We had, I think, 24 minutes of added time across the game, so it's a long time to focus - but we just lost concentration and when we play at a slower tempo, we're nowhere near as effective.
"I'm a miserable so-and-so and I should be more excited, but I've got to keep the team on the right track and we will have to be better."
England will aim to maintain their perfect start to the 2022 World Cup when they continue their campaign against the USA on Friday before tackling Wales on November 29.