Riding on Rayudu's undefeated knock of 118, Rest of India finished the fourth day's play at 296 for four taking their overall lead to a whopping 413 runs and have virtually put their hands on the trophy which they would be winning for 25th time.
With fate of the match virtually sealed, first innings centurion Suresh Raina is looking good for a second ton in the match and is batting on 40.
The only interest on fifth and final day will be whether national selectors recall Raina in the Test squad or try something out of the box by selecting Rayudu who has also scored a half century in the match.
Apart from that, Rayudu has had a good Ranji season for Baroda and also scored a century for India A against New Zealand.
The 27-year-old batsman also resurrected the Rest second innings as they were tottering at 69 for three at one stage. Rayudu added 140 runs for the fourth wicket with Manoj Tiwary, who hit a dogged 69.
During his 217 ball unbeaten knock, Rayudu has hit nine fours and four sixes --- all of them being straight lofts. This was his 14th century in first-class cricket.
Rest, began the day at 27 for 1, struggled for runs in the morning session with the Mumbai pace bowlers extracting a lot of movement.
Nightwatchman S Sreesanth (18) was run-out by a direct hit from cover point fielder Rohit Sharma. He responded to a call for a sharp single from partner M Vijay but was beaten by an agile throw from Rohit.
Vijay, scorer of a fluent century in the first innings, struggled against Dhawal Kulkarni and Shardul Thakur, edged the former once to Kaustubh Pawar, substituting for Sachin Tendulkar who was off the field for the entire day, at gully and survived.
But Thakur bowled an outswinger and Vijay tried to drive on the up only to offer a simple catch to Rohit as Rest were reduced to 67 for three.
The Tamil Nadu batsman's dismissal brought in Rayudu together with Tiwary, who looked scratchy in the initial stages of his innings and was also dropped by wicketkeeper Aditya Tare when he inside-edged Kulkarni early on.
Tiwary was also lucky not to be given out when on 4 when he was rapped in front by an in-dipper from Abhishek Nayar, who replaced Kulkarni after the latter's impressive but unlucky 8-over spell for 21 runs
Surviving this difficult phase, the Bengal batsman grew in confidence as the pitch eased out and with ball getting older, the bowlers lost sting.
Rayudu was the more aggressive player in the fifth wicket century partnership that steadied the rocking boat.
Both played freely against the spinners, when they were brought into the attack, and struck them for boundaries and sixes to up the scoring rate.
The Guntur-born Rayudu used his feet very well to negotiate the spinners after playing cautiously against the new ball bowlers in the morning when conditions were in favour of the fielding team.
The duo accelerated in the second session after they played defensively in the morning period as Rest added 108 runs in 34 overs.
They reached their individual 50's in a short span of each other, with Rayudu taking only 93 balls as compared to his partner's 135 in reaching the minor landmark.
Tiwary, unbeaten on 66 at tea, in a score of 200 for 3, departed soon after resumption of play, top-edging left-arm spinner Vishal Dabholkar to Wasim Jaffer who ran around from first slip to leg slip completing an easy catch.
In all, the batsman faced 166 balls in his 211-minute innings in which he struck 3 sixes and 5 fours.
Rayudu was joined by Raina, who got into the groove from the first ball, as the fifth wicket pair carried Rest to a position from where they cannot lose. They have added 89 runs in 136 balls before stumps.
Tendulkar, who was off the field for the entire day after striking a glorious, unbeaten 140 yesterday, can come out to bat only after the fall of the fifth wicket in Mumbai's second innings tomorrow.