Both the leaders stood in silence in front of the glass casket containing the body of the spiritual leader, who died on Sunday, and placed wreaths at his feet and sat for a few minutes at the Sai Kulwant Hall.
They heard in rapt attention Sai bhajans being sung by followers before they left the hall.
Singh and Gandhi, accompanied by Union Minister Ambika Soni, arrived here by a special aircraft and drove straight to Prashanthi Nilayam, where baba's body was lying in state in the Sai Kulwant hall.
Earlier, Andhra Pradesh Governor E S L Narasimhan, Chief Minister N Kiran Kumar Reddy, who reached Puttaparthi in the afternoon, received Singh and Gandhi at the airport and accompanied them to Sai Kulwant hall.
Sai Baba would be buried in the Sai Kulwant hall here with full state honours between 9 and 9.30 am on Wednesday, April 27. The Governor and Chief Minister will stay in Puttaparthi and attend the burial ceremonial, officials said.