The 27-year-old posted a closing 70 at the Old Course at St Andrews on Sunday to reach 22 under par and become the first Frenchman to win the tournament.
England's Southgate was alone in second a shot further back after he carded two bogeys on the back nine and failed to make the birdie he needed at the last to force a play-off.
Another Englishman Paul Waring and Swede Joakim Lagergren finished in a tie for third on 20 under, while England's Jordan Smith, Tommy Fleetwood, Tom Lewis and Matthew Jordan were in the group in a share of fifth place alongside Jeunghun Wang.
Perez is no stranger to links golf in Scotland, having spent the last 18 months living up the road in Dundee, where his girlfriend attends dental school.
And he made the most of home comforts on Sunday, carding three birdies and a solitary bogey to win on his 29th European Tour appearance.
Two-time Challenge Tour winner Perez said: "Obviously I'm very pleased.
"There are so many things that need to come together to win a golf tournament. There are so many great players that are still striving for their first win, and obviously it happened for me in my first year.
"I'm quite fortunate to be honest. Waking up this morning, you go out and you try to play as well as you can, but you don't know if somebody can go and shoot eight under – and then you lose by six and you felt like you did your job but you might be miles away.
"Obviously I felt like I had a solid day. I did my job and it was good enough, and next thing you know, you're a winner on the European Tour. You have to take it how it comes and it's a great win for me."
Perez began the day alongside Southgate at the top of the leaderboard but found himself in possession of the outright lead when his playing partner dropped a shot at the first.
His first birdie of the day came at the fifth when he got up and down from the rough to the right of the green.
Southgate leapfrogged him to the summit after reeling off a hat-trick of gains from the fifth but a six-foot birdie at the short eighth pulled Perez level with the Englishman.
Perez fell off the top of the leaderboard again when Southgate curled in from 12 feet for a birdie at the ninth to get to 23 under.
And his deficit was extended to two strokes when Perez made a bogey at the short 11th.
But a two-shot swing at the par-five 14th saw Perez join playing partner Southgate at the top once more as he tapped in his close-range birdie putt to get to 22 under, while a poor pitch shot cost Southgate a shot and the outright lead.
Perez, whose caddie is Rory McIlroy's former bagman JP Fitzgerald, took a one-shot lead to the 18th tee after Southgate bogeyed the 17th, and when they both made pars at the last, Perez secured the title.
Southgate said: "It's been a horrible season for me and this has sorted that right out and got us right back to the Race to Dubai and that's the goal for me, really.
"I think I've proven to the world this week that when I do switch it on, I can mix it with the best and I've beaten a hell of a lot of good players this week."