Tom Latham reached his fourth Test century soon after Tea before being caught by stand-in wicketkeeper Brian Chairi.
On the final day Sri Lanka needed seven wickets, Australia wanted 185 runs. And the runs were coming slowly for a nervy Australia.
India have never won two consecutive Tests in West Indies.
Left-arm orthodox bowler Jon Holland was named as replacement for O'Keefe in the Australian squad.
Wagner takes 6 for 41 to restrict the hosts to 164 on Day 1 of the first Test at Bulawayo on Thursday. NZ were 32-0 at stump.
The Indian cricketer and his actress wife welcomed the little one with their families in London.
Kusal Mendis shared 117 runs for the fifth wicket with Dinesh Chandimal (42) after Sri Lanka had slumped to 86 for four.
The visitors earned a handy lead of 86 runs before Mitchell Starc removed Perera on another truncated day.
He replace Yasir Shah after returns of 7 for 83 in the second innings of the Antigua. Root moves up to No. 2 among batsmen
Josh Hazlewood and Nathan Lyon shared six wickets bowled out Sri Lanka for 117. Australia were 66-2 at stump.