The hosts reached lunch strongly placed at 190 for four in their second innings with Khawaja 67 not out and skipper Paine unbeaten on 37.
Australia, desperate to level the series after narrowly losing the Adelaide opener, blunted India's pace attack on the grassy Perth Stadium wicket during the pivotal morning session.
India's quicks were unable to exploit the pitch’s variable bounce and lacked the energy mustered during an explosive final session on day three.
Australia resumed at 132-4 with a lead of 175 runs over India's first innings tally of 283 and dominated the first session to take control of a fluctuating match.
With only a smattering of spectators in the 60,000-seat stadium, Australia's watchful batsmen made a sedate start in the face of accurate Indian bowling and scored just 19 runs in the first hour.
Paine and Khawaja tempered their aggression, preferring to rotate the strike through sharp singles to frustrate an Indian side desperate for wickets.
Shortly before lunch, Paine and his Indian counterpart Virat Kohli were involved in a heated exchange which forced umpire Chris Gaffaney to step in.
Khawaja, Australia's most accomplished batsman, notched his first half-century of the four-test series with a clip through the leg-side to extend his team’s lead to 200 runs.
The strength of Australia's position is reflected by the fact that India have successfully chased down a fourth innings target of more than 200 runs on only 12 occasions.
In a boost for Australia's chances of batting India out of the match, opener Aaron Finch was cleared of a serious finger injury and declared fit to resume his innings on the fourth day.
Finch, who retired hurt on 25, went to hospital for X-Rays amid concern that he had suffered a fracture to his right index finger after being struck on the glove by a searing short ball from Mohammed Shami on day three.
(Reporting by Tristan Lavalette; editing by Nick Mulvenney)
