Peng outlasted French qualifier Aravane Rezai 4-6, 6-3, 6-4, while a third- seeded Kuznetsova defeated American qualifier Alison Riske 6-3, 6-2.
The two-time Grand Slam champion Kuznetsova will face another American, Christina McHale, here on Wednesday.
Meanwhile, Arn was driven out by fifth-seeded German Julia Goerges 7-5, 3-6, 6-4. Arn captured last year's ASB Classic with a victory in the final over Belgian Yanina Wickmayer, who is seeded seventh this year and downed Czech qualifier Karolina Pliskova 6-3, 6-4 on Tuesday. Wickmayer titled here two years ago and is seeking a third straight trip into the ASB final.
In other action involving seeds on the hardcourts at ASB Tennis Centre, No. 6 Italian Roberta Vinci topped Canadian Rebecca Marino 7-5, 6-4 and No. 8 Monica Niculescu of Romania breezed past American qualifier Jamie Hampton 7-6 (7-1), 6-1.
Also on Wednesday in Brisbane, top-seeded Sabine Lisicki will battle fellow German Mona Barthel in a second-rounder.
The winner of this $220,000 Australian Open tuneup will claim $37,000.