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The 29-year-old Pegula had no answer to Mertens' versatile game.
Frenchwoman Cornet, making her 63rd main draw appearance at a Grand Slam, improved her record against 2018 finalist Halep to 4-1 after the 32-year-old came through a battle lasting two hours and 33 minutes at the Rod Laver Arena.
The two will not be teaming up at Grand Slam events for the rest of 2021 as Sabalenka wants to focus on singles.
The Canadian teenager came from behind to overpower Mertens 3-6, 6-2, 6-3 and reach her first Grand Slam semifinal.
Results 1-4
