The seventh wicket duo feasted on the appalling bowling by Mumbai in which Shardul Thakur was the main culprit as he conceded 135 runs in 27 overs to help Rest adjourn for lunch at 487 for 6 after commencing the day at 330 for 5.
Raina played the spinners with splendid ease and raced from 50 to his 11th first class 100 in just 37 balls. It was the second century of the Rest innings after opener Murali Vijay's 116 yesterday.
Raina hit Rohit Sharma for three fours in an over to start the run-spree while Mithun struck Chavan for a big six over mid-wicket in the latter's first over of the day.
The 100 of the partnership came up in just 97 minutes after Raina reached his personal milestone in 140 balls.
Rest crossed the 500-mark when Raina stepped out to Dabholkar and carted him for his third six and then Mithun reached his half century off 87 balls.
Post-lunch, Rest lost their last four wickets for the addition of 39 runs, the first three wickets falling in 13 balls as Ankit Chavan who was expensive in his short stints earlier, grabbed three wickets in a spell of 4.1-1-8-3.
Chavan's victims included Raina, who was dismissed at long on while trying to loft the bowler for his fifth six, Mithun and Dabholkar. Chavan also got the wicket of last man Ishwar Pandey to finish with 3 for 56.
Mumbai began their reply 45 minutes after lunch and lost opener Aditya Tare cheaply in the fourth over when he was caught by Manoj Tiwary at gully off Ishwar Pandey.
But then Jaffer, who hit 11 fours and a six in his 126-ball knock, played some handsome drives to the off and flicks to mid-wicket off Sreesanth, who looked unimpressive till he got his revenge on the senior Mumbai batsman.
Rahane also prospered after a slow start as the duo built up the partnership. Guiding Mumbai to 61 for one at tea, the second wicket pair completed their individual 50s in the final session with Jaffer reaching his fifty in 71 balls with nine fours ahead of Rahane who did it in 90 balls with eight fours.
Just when the duo looked well set to see off the day, Sreesanth caught Jaffer in two minds to have him caught behind in the first over of his third spell.