By late 1966, Harrison's interests had moved away from the Beatles. This was reflected in his choice of Eastern gurus and religious leaders for inclusion on the album cover for Sgt. Pepper's Lonely Hearts Club Band in 1967. His sole composition on the album was the Indian-inspired "Within You Without You", to which no other Beatle contributed. He played sitar and tambura on the track, backed by musicians from the London Asian Music Circle on dilruba, swarmandal and tabla. He later commented on the Sgt. Pepper album: "It was a millstone and a milestone in the music industry ... There's about half the songs I like and the other half I can't stand."
In 1966, Harrison contributed innovative musical ideas to Revolver. He played backwards guitar on Lennon's composition "I'm Only Sleeping" and a guitar counter-melody on "And Your Bird Can Sing" that moved in parallel octaves above McCartney's bass downbeats. His guitar playing on "I Want to Tell You" exemplified the pairing of altered chordal colours with descending chromatic lines and his guitar part for Sgt Pepper's "Lucy in the Sky with Diamonds" mirrors Lennon's vocal line in much the same way that a sarangi player accompanies a khyal singer in a Hindu devotional song.
In June 1966 Harrison met Shankar at the home of Mrs Angadi of the Asian Music Circle, asked to be his student, and was accepted. Before this meeting, Harrison had recorded his Revolver track "Love You To", contributing a sitar part that Lavezzoli describes as an "astonishing improvement" over "Norwegian Wood" and "the most accomplished performance on sitar by any rock musician". On 6 July, Harrison travelled to India to buy a sitar from Rikhi Ram & Sons in New Delhi. In September, following the Beatles' final tour, he returned to India to study sitar for six weeks with Shankar. He initially stayed in Bombay until fans learned of his arrival, then moved to a houseboat on a remote lake in Kashmir. During this visit, he also received tutelage from Shambhu Das, Shankar's protégé.
In early 1966 Harrison and Lennon each purchased Epiphone Casinos, which they used on Revolver. Harrison also used a Gibson J-160E and a Gibson SG Standard while recording the album. He later painted his Stratocaster in a psychedelic design that included the word "Bebopalula" above the pickguard and the guitar's nickname, "Rocky", on the headstock. He played this guitar in the Magical Mystery Tour film and throughout his solo career. In July 1968, Clapton gave him a Gibson Les Paul, which Harrison nicknamed "Lucy". Around this time, he obtained a Gibson Jumbo J-200 acoustic guitar, which he subsequently gave to Dylan to use at the 1969 Isle of Wight Festival. In late 1968 Fender Musical Instruments Corporation gave Harrison a custom-made Fender Telecaster Rosewood prototype, made especially for him by Philip Kubicki. In August 2017, Fender released a "Limited Edition George Harrison Rosewood Telecaster" modelled after a Telecaster that Roger Rossmeisl originally created for Harrison.
By the mid-1960s Harrison had become an admirer of Indian culture and mysticism, introducing it to the other Beatles. During the filming of Help! in the Bahamas, they met the founder of Sivananda Yoga, Swami Vishnu-devananda, who gave each of them a signed copy of his book, The Complete Illustrated Book of Yoga. Between the end of the last Beatles tour in 1966 and the beginning of the Sgt Pepper recording sessions, he made a pilgrimage to India with his wife Pattie; there, he studied sitar with Ravi Shankar, met several gurus, and visited various holy places. In 1968 he travelled to Rishikesh in northern India with the other Beatles to study meditation with Maharishi Mahesh Yogi. Harrison's use of psychedelic drugs encouraged his path to meditation and Hinduism. He commented: "For me, it was like a flash. The first time I had acid, it just opened up something in my head that was inside of me, and I realized a lot of things. I didn't learn them because I already knew them, but that happened to be the key that opened the door to reveal them. From the moment I had that, I wanted to have it all the time – these thoughts about the yogis and the Himalayas, and Ravi's music."
In line with the Hindu yoga tradition, Harrison became a vegetarian in the late 1960s. After being given various religious texts by Shankar in 1966, he remained a lifelong advocate of the teachings of Swami Vivekananda and Paramahansa Yogananda – yogis and authors, respectively, of Raja Yoga and Autobiography of a Yogi. In mid-1969, he produced the single "Hare Krishna Mantra", performed by members of the London Radha Krishna Temple. Having also helped the Temple devotees become established in Britain, Harrison then met their leader, A.C. Bhaktivedanta Swami Prabhupada, whom he described as "my friend ... my master" and "a perfect example of everything he preached". Harrison embraced the Hare Krishna tradition, particularly japa-yoga chanting with beads, and became a lifelong devotee.
Before his religious conversion, Cliff Richard had been the only British performer known for similar activities; Richard's conversion to Christianity in 1966 had gone largely unnoticed by the public. "By contrast," wrote Inglis, "Harrison's spiritual journey was seen as a serious and important development that reflected popular music's increasing maturity ... what he, and the Beatles, had managed to overturn was the paternalistic assumption that popular musicians had no role other than to stand on stage and sing their hit songs."
Harrison married model Pattie Boyd on 21 January 1966, with McCartney serving as best man. Harrison and Boyd had met in 1964 during the production of the film A Hard Day's Night, in which the 19-year-old Boyd had been cast as a schoolgirl. They separated in 1974 and their divorce was finalised in 1977. Boyd said her decision to end the marriage was due largely to George's repeated infidelities. The last infidelity culminated in an affair with Ringo's wife Maureen, which Boyd called "the final straw". She characterised the last year of their marriage as "fuelled by alcohol and cocaine", and she stated: "George used coke excessively, and I think it changed him ... it froze his emotions and hardened his heart." She subsequently moved in with Eric Clapton, and they married in 1979.