Singh, who had contested the last Lok Sabha polls from Bhopal, had lost to BJP candidate Pragya Singh Thakur, while Scindia had unsuccessfully contested the polls to the Lower House of the Parliament from Guna constituency, considered the pocketborough of his family.
The entry into the Rajya Sabha of these two influential leaders from the state comes three months after the collapse of the Kamal Nath-led Congress government.
Till early this year, Singh and Scindia were being seen as Congress's candidates for the Rajya Sabha polls from the state.
Considering Congress's strength in the House when the the party was in power in the state (during the previous Kamal Nath government), both of them could have won the seats easily.
Congress insiders say that both the leaders wanted their names on top in the pecking order of their party's nominee list.
Scindia was averse to the idea of playing second fiddle to Digvijaya Singh as fearing that the latter's camp could rock his boat, the party sources said.
Scindia wanted to be the first preference candidate of the Congress, they said.
The BJP sensed an opportunity there and decided to exploit the rift between the two leaders.
Following their differences, the Congress's central leadership intervened and tried to broker peace between them, but in vain, a top party leader said on condition of anonymity.
Reportedly, Scindia had long been upset with the Congress, as he believed that former chief minister Kamal Nath and Digvijaya Singh were working in tandem to sideline him.
Senior Congress leader Dipak Babaria said that when he was party general secretary in-charge of MP, both Singh and Scindia were assured nominations for the Rajya Sabha seats.
"At that time, we had numbers on our side. And both of them could have sailed through. The reservations that Scindia had in his mind had also been cleared," he said.
Howevre, Scindia finally left the Congress in March and joined the saffron party. Soon after, 22 Congress MLAs, many of whom loyal to him, resigned, which reduced the Congress to a minority in the state. Their move cleared the way for BJP to come to power in MP.
Kamal Nath resigned as chief minister on March 20 and BJP installed Shivraj Singh Chouhan as the CM once again.
Political observers say that the tussle between Digvijaya Singh and Scindia was one of the reasons behind the fall of the 15-month-old Congress government in the state.
Scindia had later said in Bhopal that he left the Congress as he was slighted there.
After his entry into BJP, which could have otherwise won only one Rajya Sabha seat from the state in th polls held on Friday, ended up winning two.
Speculation is rife that the BJP might reward Scindia with a cabinet berth in the Union ministry.
Digvijaya Singh, too, has made it to the Upper House despite rumblings in sections of the party, especially the young turks.