Despite having to come off at half time in Friday's 4-0 triumph over Malta due to a blow to the ankle, Saka was passed fit to start at Old Trafford alongside Harry Kane and Marcus Rashford.
On the back of his best-ever goalscoring season for Arsenal, in which he struck 15 times in all competitions, Saka earned a slice of personal history with his first-ever senior hat-trick at the Theatre of Dreams.
The 21-year-old opened his account for the evening with an arrowed finish into the roof of the net before doubling his tally two minutes into the second half with a stunning half-volley into the top corner from Trent Alexander-Arnold's long ball.
Saka completed his hat-trick in the 51st minute, slotting home into the bottom corner from Kane's through ball to become the first Arsenal man to net an England treble since Theo Walcott against Croatia in 2008.
The Hale End graduate was given a standing ovation by his teammates and supporters as he came off just before the hour mark and claimed that he would remember his first hat-trick for the rest of his life.
Speaking to the press after the demolition job, Southgate revealed that Saka had been struggling with an Achilles issue for the past few weeks and was overjoyed to see the winger push through the pain to enjoy a memorable evening.
"I am delighted for him. He's had a slightly sore Achilles - for a few weeks - and it's another one where it would have been easy to pull out of the camp and miss out on a night like this that I'm sure will live with him forever. When you have one of the best nights of your life it's a reminder to everyone to go through these things," Southgate said.
When asked if Saka could soon be classed as an "elite" footballer, the England manager responded: "I think he is already there.
"He broke into a team [Arsenal] having a difficult time and performing at a high level, then when the team was playing well he's still performing. That says everything. He's exceptional to work with.
"For [all of] the players to have the mentality they have to work, at the late stage of this monster of all seasons, there was every excuse to do that and they've not done that."
Saka's hat-trick was not the only first for England on Monday night, as Manchester City midfielder Kalvin Phillips came off the bench to open his account for the Three Lions in the second half.
Kane also scored for the sixth England game running with a brace of his own at Old Trafford, while Rashford made the net bulge at his home ground in the first half.
England's crushing win sees them remain top of Group C with 12 points from four games against Italy, North Macedonia, Malta and Ukraine, the latter of whom are six points behind in second place with a game in hand.
Southgate's side will reconvene in three months to face Ukraine on September 9, three days before they meet Scotland at Hampden Park in a 150th anniversary fixture.