The veteran musician read a specially-written poem in honour of the spiritual leader, who turns 80 years old on 06 July (15), as part of her set, before inviting him to join her.
Smith then led the audience in a rendition of Happy Birthday and presented the Dalai Lama with a fruit-topped cake, which he cut and sampled to cheers from the audience.
He told revellers, "Thank you, thank you. I hugely appreciate so many people's expression of warm feelings. I very much appreciate it. I dedicate my body, speech and mind to the wellbeing of others, as my main daily practice, so when the people show this warm feeling, that gives me more enthusiasm."
The Buddhist leader was attending the event in south-west England to talk to festival-goers in the Green Fields part of the site, where his Tibetan Monks performed in 2013. He was also treated to a tour of the site by festival bosses.
During a question-and-answer session with BBC executive Alan Yentob, the Buddhist leader told followers and fans alike, "While you are here, enjoy the joyfulness here. But you should remember on this same planet are human beings being killed by human beings."
He added, "I noticed when I was coming in by car that the people are old and young, everybody seems to be having fun. People are happy and joyful. My friend asked me to come to his great festival: a festival of people. Not necessarily a festival of the government, or of politicians. This, I think truly, is a festival of the people."
Yentob later told NME.com that chatting to the Dalai Lama was "a one-off... like nothing I’ve done before", adding, "He’s a very sweet natured man with a lot of humanity and compassion and that’s his big thing, so it was a privilege to be here and see thousands of people starting to emerge, and the crowd grew and grew."