The Mumbai Indians took control of the match after a poor first innings by the Indian pacers.
Ajinkya had a couple of good catches to end the day and added to his tally with five wickets.
He scored nine fours, eight sixes and seven sixes in a sensational display.
India have now won their first Test series against Pakistan since their last Test match in 2017, and they have now scored more runs than Pakistan at the SCG since that match.
They have also lost one Test match, against England, to the Pakistanis.
They were in their best form, scoring more runs per over and bowling with more power, with Ajinkyan and Rahane leading the attack.
Rahane is a man of the hour with three sixes, four sixes to be exact, in his career.
He has now played at the MCG, the Oval and other venues in Australia.
He is also a member of the Indian Test team and is regarded as one of the most promising young batsmen in the country.
In the opening match of the series against England on Monday, Ajinkyu had scored a brilliant 111 not out in his final over to finish off the innings.
Ajankyan is also among the top five in the ICC rankings.
India’s performance in the first Test was one of its best of the season.
They started well in their opening innings but lost the momentum.
They conceded seven wickets in the opening innings, but managed to win the toss and took control in the second innings.
This was a poor performance by the Pakistan side, who had won the toss.
Their batsmen struggled to find their rhythm, especially after the pacers began to bowl out of control.
The first half saw India go to the crease for three quick sixes but they were unable to find any form and ended up losing the game.
Rahane is known to be a very good bowler and had taken his first hundred against Pakistan at The Oval in January, and he added to it in the match.
Ajinkyan is a very strong bowler, and has also scored three six in his first innings.
He can take a lot of wickets and scores lots of runs, but he is also very good with the ball.
It was an important win for India, but Pakistan will have a lot to work on against their arch-rivals in the next match.