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Malinovskiy's fantastic winner was just reward for a scintillating Marseille display at Stade Velodrome.
Igor Tudor's team had 12 shots in the first half and took the lead through Alexis Sanchez's 31st-minute penalty, which was cancelled out by Sergio Ramos' header.
Ramos thought he had sent the tie to penalties when he headed home in stoppage time, but the offside flag came to Marseille's salvation.
A frantic opening set the tone. Pau Lopez denied Nuno Mendes before Gianluigi Donnarumma tipped over from Cengiz Under, saved Malinovskiy's stinging effort and watched Sead Kolasinac's strike arrow just wide.
PSG's luck ran out when Ramos tumbled into Under just inside the area – Sanchez coolly sending Donnarumma the wrong way from the spot and becoming the first Marseille player to net in a home Classique since Florian Thauvin in 2017.
Neymar struck the right-hand post with a superb low shot, though the woodwork then came to PSG's rescue when Under clipped the crossbar after Donnarumma unconvincingly thwarted Jonathan Clauss.
Marseille was made to pay for its profligacy on the cusp of half-time, Ramos nodding in from Neymar's corner.
Parity lasted just 12 minutes, though, with Malinovskiy lashing a venomous half-volley beyond Donnarumma from the edge of the box.
Valentin Rongier's wonderfully timed tackle prevented Mendes going through on goal as PSG hunted an immediate response.
Marseille was immensely fortunate Ramos strayed offside before heading in from a cross-shot that hit the bar, though it ultimately deserved its luck as 14-time Coupe de France winner PSG crashed out at the same stage as last season.