Max Jowitt crossed early on after good work by Craig Hall, but three quick tries by Tony Gigot, Dave Taylor and Justin Horo put the hosts in control.
Wakefield drew level at 18-18 at the break when Jonny Molloy powered over and Hall touched down.
The teams both scored two further tries but Pat Richards missed a late kick with his side trailing by two at 30-28.
And Wakefield, who were already assured of their place in the top eight, held on for a victory which ends a three-match losing run.
The Wildcats had regained the lead after an even first period when Bill Tupou made the most of some quick thinking by Hall to go over.
Catalans responded again when Morgan Escare ran onto a Lucas Albert kick.
Mikey Sio then crossed for the visitors and the reliable boot of Liam Finn made it 30-24, but although Fouad Yayha scored in the corner, Richards' missed conversion proved costly for Catalans.
Catalans Dragons: Escare, Yaha, Garcia, Duport, Richards, Gigot, Albert, Baitieri, Taylor, Horo, Maria, Pelissier, Casty.
Substitutes: Bousquet, Da Costa, Mason, Navarrete.
Wakefield: Jowitt, Lyne, Arundel, B Tupou, Hall, Miller, Finn, Simon, Moore, Arona, Ashurst, Molloy, Sio.
Substitutes: Scruton, A Tupou, Walton, Fifita.
Att: 8,562.
Ref: Chris Campbell (RFL).

The round £1 will be legal tender alongside the new, more-secure coin until 15 October.
The public are being urged to use their current £1 coins or bank them before they lose their legal tender status.
The government estimates around a third of the £1.3 billion worth of coins stored in piggy banks or saving jars around the UK are the current £1 style.
Some of those returned by the public will be melted down and used to make the 12-sided version.
The new style was announced in the 2014 budget and has been billed by the Royal Mint as "the most secure coin in the world".
Its introduction will come as a new set of coin designs are also brought into circulation, celebrating the achievements of Jane Austen and Sir Isaac Newton.
The Royal Mint said the new designs have a "strong pioneering theme" and will start appearing this spring.
A Jane Austen £2 coin will celebrate the author 200 years after her death, while another £2 version will remember the Royal Flying Corps.
A 50p coin will mark the achievements of mathematician Sir Isaac Newton, a one-time Master of the Royal Mint.
Dr Kevin Clancy, director of the Royal Mint Museum, said: "This is a particularly significant year in Royal Mint history as we welcome in the new 12-sided £1 coin, with its innovative security features.
"This year we also mark the achievements of Jane Austen, Sir Isaac Newton and the Royal Flying Corps - all pioneers in their own field."
Wakefield moved up to sixth in Super League after edging a thrilling topsy-turvy encounter with Catalans Dragons.
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The new 12-sided £1 coin will enter circulation on 28 March, the government has said.