Kurt Elling and Sheila Jordan, Queen Elizabeth Hall

Just occasionally an artist hits the truth of the song in such spectacular fashion that it makes you feel with ever greater intensity what it means to be human.

Last night, vocalist Sheila Jordan's performance of the Jimmy Webb standard, “The Moon is a Harsh Mistress”, a song she recorded on her 1999 album Jazz Child, achieved exactly that: a shatteringly personal account, bookended by an improvisation on a native American theme, both the pathos and power of the song were extraordinary. I'm sure I wasn't the only one who was wiping away tears.

With a career that stretches back to the 1940s and the heady days of bebop - and a friend of Charlie Parker, Charles Mingus, Don Cherry and George Russell - Sheila Jordan (pictured below right) is one of the bona fide legends of the music. The first ever singer to record for Blue Note (the classic Portrait of Sheila, released in 1962), earlier this year she was given a lifetime achievement award from the NEA Jazz Masters.

A capacity QEH audience navigated the chorus riff of 'Workshop Blues' with a surprising ease

Jordan's set took in a brace of songs from her Blue Note debut, “Hum Drum Blues” and the Bobby Timmons/Oscar Brown Jr. classic “Dat Dere”, recorded by everyone from Art Blakey to Rickie Lee Jones, in which she perfectly captured a child's excitement at a trip to the zoo (“Can I have that big elephant over there?”). Appearing with the superb trio of pianist Brian Kellock – who dazzled throughout with his sparkling, searching solos - bassist Kenny Ellis and drummer Stu Ritchie, from the medium swing of “Wouldn't it Be Lovely” to the gentle bossa of “All or Nothing at All”, Jordan's love of the music stole the audience's heart.

Also featuring some rather wonderful singing by a capacity QEH audience – navigating the chorus riff of “Workshop Blues” with a surprising ease (I suspect that the odd singer or two might have been in attendance) – Jordan signed off with Gordon Jenkins' “Good-Bye”, for which she improvised the concluding lyrics: “If I don't see you again, have a beautiful life”.

In the second half, Kurt Elling performed a captivating set culled mainly from his latest release 1619 Broadway – The Brill Building Project. The eclectic song list included a brilliant reimagining of “Come Fly With Me” (great work here from Elling's long-standing collaborator, pianist Laurence Hobgood), Sam Cooke's crossover hit “You Send Me” featuring a killing groove from drummer Brian Connor, and the bold reharmonisations of Bacharach and David's “A House is Not a Home”.

As always, Elling had some surprises up his sleeve, including a wonderful unaccompanied piece which built up layer upon layer of vocal lines into a swirling contrapuntal stream, before launching into a bracing “On Broadway”. Doc Pomus's “Lonely Avenue”, a song associated with the Brill Building which doesn't feature on Elling's album, was most effectively stripped down here to just bass (Clark Sommers) and voice, with backing vocals from the band (guitarist John McLean added the subtlest textural hints towards the end). Elling concluded with one of his great crowd-pleasers, “Nature Boy”.

For an encore, Kurt and Sheila dusted down a playful “I'm In the Mood for Love”, in which Jordan made up new lyrics on the spot, including the brilliant (directed at Kurt) “I wish I could have him. I mean as my son, not my lover. I could be his grandmother". Pretty good going for a singer who will be 84 this Sunday. Many happy returns, Ms Jordan.

• This concert will be broadcast in Radio 3's Jazz Line-Up on Sunday 6 January 2013.
• The London Jazz Festival continues until 18 November.