The song, which mixes the MC's freshly recorded verses with a jazzy Winehouse hook, hit New York City's Hot 97 on Wednesday.
Last month, Nas, born Nasir Jones, revealed that Winehouse's "Back to Black" song "Me and Mr. Jones" was about him.
"I don't really remember if [producer] Salaam [Remi], who was really close to her, who introduced us, if he told me about it or not," he told XXL. "But I heard a lot about it before I even heard the song."
Remi produced "Like Smoke," which was initially recorded in 2008. Winehouse and Nas shared a birthday and were reportedly planning a dual party before her untimely death in July from alcohol poisoning.
The 12-track "Lioness," a compilation of demos, covers and unreleased material, is due Dec. 5.