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Nawaz gave away 16 runs off the final over. The left-arm spinner was also guilty of bowling two wides and a no-ball amid mounting pressure at the MCG.
Excitement is already building for the October 23 T20 World Cup blockbuster between the former champions in Melbourne but Indian captain Rohit sought to downplay the hype around one of cricket's greatest rivalries.
The hosts chased down a target of 200 runs in style with Babar scoring 110.
Shan Masood has been given maiden call-up while Shaheen Afridi has been included.
Babar is an ardent supporter of Kohli.
All eyes will be on Kohli when India meet Pakistan in their Asia Cup opener in Dubai on Sunday
Malik, who played the last of his 124 Twenty20 Internationals against Bangladesh last November, has impressed in Pakistan's domestic T20 league.
The series is being played against the backdrop of Sri Lanka's worst economic crisis since independence.
While Kohli's place in the team has been debated by fans and legends, Babar has extended his support via social media.
The Asian Cricket Council is planning to revive the Afro-Asia Cup.
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