Jadeja picked up Matthew Wade cheaply to peg Australia back.
Smith got to his first fifty of the series.
Labuschagne fell for 91, falling just short of his century with Jadeja ekeing out an edge to Rahane.
Labuschagne and Smith added 100 runs for the third wicket.
Rain interrupted twice in the first session on Day 2 in an extended morning session.
Steve Smith scored his first century of the series, keeping Australia afloat while wickets fell around him.
Jadeja returned a four-wicket haul before running out Steve Smith to end Australia's innings for 338.
Rohit Sharma and Shubman Gill started positively for India adding a 50-plus stand for the opening wicket.
Gill fell after his maiden Test fifty.
Hazlewood first got Rohit picking up a sharp catch in his followthrough after which Gill was caught at gully. Rahane and Pujara steadied the innings as India went to stumps at 96/2, trailing by 242.