The 30-year-old Vijay, who missed a century by one run in the second innings in Adelaide, notched up his fifth Test ton to guide India to a good position on a hot day at the Gabba.
Vijay was dropped by Shaun Marsh on 36 off paceman Mitchell Johnson but he capitalised on the reprieve by punishing the Australians, scoring 144 off 213 balls.
The right-handed opener got good support from Rahane (batting 75) as the duo shared a 124-run stand for the fourth wicket with the Australian pacers struggling to find any rhythm in the hot and humid conditions.
Vijay was again dropped on 102 by Shaun again off Johnson but he could not cash in on the second chance.
Apart from the two chances he gave to the Australians, Vijay stroked well throughout in his innings which he paced very well.
He looked at ease against the Australian pace battery and effortlessly drove the fast bowlers. He was hardly troubled by Nathan Lyon untill he charged the spinner to be caught behind.
Skipper Mahendra Singh Dhoni had taken a bold decision to bat on the green and pacy Gabba wicket and his decision stood vindicated as Indian batsmen responded well to the call.
Rahane was batting on well and giving him company was Rohit Sharma (26 batting) when stumps were drawn for the day.
Shikhar Dhawan (24) was a disappointment as he yet again failed but Cheteshwar Pujara (18) was unlucky to be given caught behind off debutant Hazlewood while dodging a high ball as it touched his helmet’s visor and not his gloves.
Virat Kohli, who scored two hundreds in the lost Adelaide Test, made a good start but was guilty of cutting a ball which was too close to the body and was caught behind off Hazlewood.
PTI CN AT MRM