The overnight co-leader carded a bogey-free round of 65 on Sunday to finish the tournament on 17 under par, one shot ahead of former US Amateur Champion Fitzpatrick, with Tyrrell Hatton one shot further back on 15 under.
Fitzpatrick opened his final round with a bogey at the par four first, before firing four birdies in his next eight holes to hold a one shot lead at the turn.
But a bogey at the 11th hole saw the 20 year old slip back to 14 under par alongside Willett, who fired three consecutive birdies from the 13th to put himself in the driving seat. The Sheffield native then finished his round with three straight pars to claim his second title of the campaign, following his win in the season-opening Nedbank Golf Challenge.
Victory moved Willett to second in The Race to Dubai behind leader Rory McIlroy, and could well see him climb into the top 25 of the Official Golf World Ranking.
"It was a great day," said Willett. "Yesterday was a bit disappointing, but today I played some really good golf. Matt [Fitzpatrick] was snapping at my heels all day, so I'm delighted to get the job done.
"He played some great golf and really kept the pressure on me. But it probably made it a bit easier to be honest, because it meant I couldn't lose concentration even for a minute. With a bigger lead you can take your foot off the gas a bit, but today I knew I had to keep attacking and committing fully to shots, and luckily enough it turned out well in the end.
"Winning is always tough, and the heart rate on 18 was pretty high. Having a lag putt is almost trickier than trying to hole one sometimes, so I was very relieved to see it stop a foot or two from the hole.
"The season has been very, very good. Two wins and good performances in Majors and World Golf Championships is more than I could've hoped for really, but I've worked really hard so it's nice to get the rewards for it."
The lowest score of the day went to Hatton, who carded an eagle and six birdies on his way to an eight under par 62.
That was good enough for third place, one ahead of his playing partner Pelle Edberg, who shot a round of 63.
World Number Ten Sergio Garcia, appearing at Crans-sur-Sierre for the first time in nine years, closed with a rouind of 64 to climb to seventh place.
Richard Green was the leading Australian when he finished 10th.
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