The Frenchman, who won the Legends Open de France last week, bettered Brier’s bogey on the first trip back down the par-4 18th hole with a good up and down from the bunker for par after the pair were tied on nine-under after 54 holes at Royal Aberdeen.
The duo were paired together in the final round and both posted six-under 65s to reach nine-under, one shot clear of Switzerland’s Andre Bossert and 2018 champion Gary Orr.
After triumphing on the first extra hole, Levet completed a double tartan triumph after landing the Scottish Open title in 2004.
“I’m very happy, two weeks in a row is unreal,” he said. “Nobody beat me for two weeks, it’s a joke. My game is on, I knew it from the start of the season.
"I’ve been playing really, really solid golf and my putter was not very good but now my putter is extremely good. It’s a big weapon I’ve got in my bag and it shows in the results.
“I won the Scottish Open and then the week after for three days I was in lead at The Open so I have done this before but I know that you get exhausted so, with experience, you overcome it. This is the first time I’ve won back-to-back and for me, it’s unreal. I’m also moving up the rankings, so it’s good.
“As soon as they tell you you’re playing Royal Aberdeen, you just sign up. It’s a links course, which I love, and it basially pushes you to the limit. You have to have your game on, distance control has to be spot on all the time and you need the bounces.”
Bossert tied the course record with a seven under par round of 64, to share the feat with eight-time Major Champion Tom Watson and former European Tour player turned referee Derrick Cooper, who was the Tournament Director at Royal Aberdeen this week.
Englishman Peter Baker finished fifth on seven-under, while defending champion and tournament host Paul Lawrie came sixth on six-under.