Richard Thompson played his first Martha’s Vineyard concert Thursday night, more than half a century after beginning his career in the British band Fairport Convention.

His performance, at the Old Whaling Church in Edgartown, was a long time coming, and Mr. Thompson made it worth the wait with a riveting two-hour solo show. Every pew in the church was packed, along with an extra row of chairs in front, when Mr. Thompson took the stage just after 8 p.m. to a roar of excitement from the crowd.

With his signature black beret and white Van Dyke beard, the singer-songwriter and guitarist was ready to rock in a sleeveless denim vest over black T-shirt and jeans. He carried just one guitar, a handmade Lowden six-string acoustic that he’s been playing for so long his right forearm has worn away the finish on the body.

It’s all he needed to fill the room. With that guitar and his unmistakeable, mahogany-toned voice, Mr. Thompson held the audience spellbound through 20 original songs, the traditional Irish ballad She Moved Through the Fair and a heartfelt cover of Sandy Denny’s Who Knows Where the Time Goes, which she recorded with him in Fairport in 1969.

From Fairfield Convention to the Old Whaling Church. — Ray Ewing

“Yes, I really am that old,” he told the audience in his introduction, adding slyly “and... some of you are, too,” to widespread laughter.

Ms. Denny, who died in 1978 at 31, was “perhaps the greatest singer England ever produced,” Mr. Thompson said. “If my version of this leads you to YouTube to check out Sandy’s version, then my work is done.”

At 70, Mr. Thompson remains as powerful a performer as when he was turning heads in his teens, a blazing guitarist who chose the stinging sound of a Fender Stratocaster guitar over the rounded tones of Eric Clapton’s Gibson and has followed his own path ever since.

Thursday’s concert often mined the darker side of human relationships, a central theme in Mr. Thompson’s work. His rich singing voice and quicksilver guitar playing drove home the emotional weight of the lyrics in songs like The Ghost of You Walks, The Dimming of the Day, I Misunderstood and A Love You Can’t Survive.

Romance, in all its moods, is always on Mr. Thompson’s radar. His delicate picking burnished the tender nostalgia of Beeswing, while the uptempo Valerie was shot through with gleaming guitar leads.

On Tear-Stained Letter, a bitterly rollicking number from the first album he made after breaking up with wife and musical partner Linda Thompson in the early 1980s, Mr. Thompson divided the audience into sections to sing a clap along. He also performed solo versions of two songs from his new band album, 13 Rivers, a brooding, urgent The Storm Won’t Come and an edgy The Rattle Within.

Near the end of the show, Mr. Thompson welcomed his new partner, New Jersey singer-songwriter Zara Phillips, to the stage for a pair of swaggering classics he originally recorded with Linda Thompson: I Want to See the Bright Lights Tonight and Wall of Death.

Ms. Phillips also sang harmony on two 21st-century songs by Mr. Thompson, She Never Could Resist a Winding Road—which has been recorded by Joan Baez—and the mordant My Enemy.

Thursday’s show was presented by the Martha’s Vineyard Summer Concert Series, which brings Steve Earle and the Dukes to the Old Whaling Church for an 8 p.m. concert July 9. Brooklyn-based husband and wife country duo the Mastersons will open.