"He came to seek my blessings...we exchanged sweets, "said Mr Patel, who is 82.
Mr Modi can certainly afford to be gracious. Mr Patel exited the BJP before the elections to found the Gujarat Parivartan Party (GPP). He has made little impact, winning just two of the 182 seats he contested.
For months before he left the BJP, Mr Patel, who has also served as chief minister of Gujarat, had complained publicly about Mr Modi's intolerance for dissent. Their rivalry has been robust.
Mr Patel was the chief minister of Gujarat when the BJP flew in Mr Modi from Delhi in October 2001 to replace him. Mr Modi has headed the government ever since.
Mr Patel, a veteran member of the BJP's parent body, the Rashtriya Swayamsewak Sangh or RSS, has won his own election from Visavadar constituency, but his party did not impress even in the Saurashtra region, which is dominated by his rich and powerful community.
His campaign reportedly received tacit ground support from a section of the RSS, which faults Mr Modi for ignoring its instructions.