Replying to Australia's 572-7 declared, Rahul was on 106 not out at the break with his captain Virat Kohli, unbeaten on 67, alongside him in a partnership of 137 that survived the entire second session.
Australia, 2-0 up in the four-match series, will feel that Rahul should also have been dismissed for 46 just before lunch but Steve Smith dropped the ball after the opener had ballooned it into the air with a top edge.
The Australia captain made it clear he believed the wire that holds the overhead TV camera -- Spidercam -- in place had prevented him from taking the catch.
"It's clear the ball did not hit the camera or its supporting wires," Broadcaster Channel Nine and Cricket Australia later said in a joint statement.
"Captain Steve Smith was distracted by one of the wires in his eye line. Both CA and Nine will continue to work together on the use of Spidercam in the broadcast coverage and will take on board any player feedback as necessary."
There was no interference, however, when Smith, at second slip, dropped a relatively simple chance to remove Kohli off the bowling of Mitchell Starc just before tea.
Rahul made the most of his reprieve even if none of the Indian batsmen really cut lose as they approached their assault on the Australian tally with some caution.
The 22-year-old, who endured a torrid test debut with just four runs in two innings in the draw in Melbourne last week, reached the milestone with his 11th four just before tea having faced 253 balls.
Rahul had survived another scare when he was nearly run out soon after Rohit Sharma had departed for 53, the only wicket to fall in the first two sessions.
Sent back by Kohli after calling for a single, Rahul fell over halfway down the wicket and, leaving his bat behind, had to launch himself head first towards the safety of the crease.
Smith stood with his hands on his hips showing his disappointment at Australia's failure to snap up the chance on a Sydney Cricket Ground track that still looked excellent for batting.
