Shankar's album 'The Living Room Sessions Part 1' saw off competition from Anoushka's 'Traveller', Amadou & Mariam's 'Folila', Daneil Ho's 'On A Gentle Island Breeze' and Hugh Masekela's 'Jabulani'.
Anoushka accepted the award on the sitar maestro's behalf at music's biggest night at the Staples Center here, saying, "Its OK to lose to your father."
Shankar passed away on December 11 at the age of 92 following a heart-valve replacement surgery in San Diego.
Anoushka was also on hand Saturday to receive the Lifetime Achievement award alongwith Shankar's other daughter Norah Jones at the Academy's Special Merit Awards celebration.
Beatles icon Paul McCartney won the Best traditional pop vocal album for his 'Kisses On The Bottom'.
British soul singing sensation Adele, who swept last year's awards with six wins, was presented with the Best Pop Solo Performance Grammy by Jennifer Lopez and Pitbull for a live rendition of her hit song 'Set Fire To The Rain'.
Australian musician Gotye emerged a big winner at the Grammys this year, taking home three trophies - Record of the Year and Pop/duo group performance for his song 'Somebody That I Used to Know' and Alternative music album for 'Making Mirrors'.
Album of the Year award went to 'Babel' by Mumford & Sons, whose performance at the big night of music was introduced by superstar Johnny Depp.
American band Black Keys also won three awards - best rock performance and best rock song for 'Lonely Boy', while their 'El Camino' was named the best rock album.