Runs came slowly for India in the face of tight bowling but there was controversy as television's "spidercam" appeared to contribute to an Australian dropped catch on in the final Test on Thursday. (Scorecard | Day 3 Blog)
Australia messed up two chances to dismiss Rahul on 41 and 46, the second one possibly caused by the positioning of spidercam held up by cables above the field.
The first went astray as Kohli was beaten by Nathan Lyon's flight and the ball fizzed past wicketkeeper Brad Haddin with Rahul charging down the pitch for a run.
Rahul was sent back then fell over and lost his bat yet still managed to scramble home and beat Haddin's delayed throw to the non-striker's end.
Skipper Steve Smith stood glaring at Haddin with his arms outstretched at the botched chance as India had a big let-off.
But it was Smith who was next at fault when he put down Rahul behind the wicket three overs before lunch after the Indian skied a pull shot.
Smith was seen to mouth an expletive to team-mates, which suggested he was distracted by the cables connecting the spidercam aerial TV camera.
Rahul appeared to have another chance earlier in the session when the Australians appealed for a catch by Joe Burns at bat-pad off spinner Lyon but umpire Richard Kettleborough was unmoved.
Infrared TV replays showed the ball may have brushed a glove and off the thigh guard to Burns, who did not refer the catch to the third umpire.
Sharma was out attempting to sweep Lyon only to get a bottom edge on to his stumps for 53 off 133 balls, ending a stubborn 97-run partnership with Rahul.
Only 51 runs came off 30 overs in the third day's slow-moving morning session in Sydney for the loss of Rohit Sharma's wicket.
India went to lunch at 122 for two and trail Australia by 450 runs with Lokesh Rahul unbeaten on 50 and skipper Virat Kohli on 16.