It was Kerala's third win on the trot in Elite Group E, while Delhi suffered their first loss in three games.
Australia exploited India's injury woes and punished their poor fielding to reach 274/5 at the close of a steamy opening day of the fourth Test.
The pacer forced off the field during the second session of the opening day due to groin pain and taken for scans.
The left-arm pacer, who came to Australia as a net bowler, became the first Indian cricketer to make his international debut across all three formats during the same tour.
India will give their walking wounded every chance to prove their fitness for the series-decider, batting coach Vikram Rathour said.
A native of Thalankara in Kasaragod district, the 26-year-old has become an overnight star with the match-winning hundred against Mumbai.
The New Zealand captain reached the milestone off just 36 balls in the domestic Super Smash competition.
Pucovski has failed to recover from a shoulder injury in time for the decisive fourth Test against India.
The 26-year-old's century, the first by a Kerala player in the Mushtaq Ali Trophy, set up the state's maiden win over Mumbai at the senior level.
The opener brought up his hundred off just 37 balls.