Sonny Rollins, Barbican Hall, London

He blew like the legend he is – so why am I blubbing?

Tears started rolling as soon as the saxophone legend Theodore "Sonny" Rollins took the stage, and continued for much of the 90- minute performance.

Needless to say, the tears were mine, not his. They weren't entirely due to seeing this strong, vigorous man's physical discomfort, either, evident in his stooped posture and awkward limp across the floor; nor to the awesome love-vibes of the blissed-out crowd roaring out a welcome to the leonine figure in orange silk shirt and shades. No, this was more like Greek tragedy in the making.

At 79 years of age, Rollins – whose breath-power had, in previous shows, almost blown the roof off the building – looked vulnerable as never before. In the past, he would start with a full-tilt assault on the opening number where the solo could go on for 10 minutes or more without repetition, ideas cascading from his horn like a writer's perfect prose, the texture thickened with Joycean musical puns and quotes. Tonight, it was a decidedly low-key beginning, Rollins content with a few halting choruses before passing the tune over to the band. "Oh Sonny!", we thought. "Has it come to this?". But then – sly old fox that he is – Rollins took the second tune at a furious pace, heating up with a longish solo where his tone sounded as hard and unyielding as any tyro's. From then on, although the pace sometimes slackened, this remained a masterly show full of wit and guile as well as pathos.

The reduced firepower of the leader also led to compensations. A Rollins concert has never been about the band, who are there to back him up, taking up any slack where necessary. Some of them have even grown old in the service, like the bassist Bob Cranshaw who's been with him for close to half a century; or the trombonist Clifton Anderson who, as Rollins's nephew, really is part of the family. Now, tender solicitude for their employer's welfare is evident in every phrase and gesture as the lead is tossed between musicians like a basketball. Bobby Broom on guitar, and Kobie Watkins on drums, were particularly outstanding, and when the poker-faced percussionist Sammy Figueroa got his turn late in the show, he nonchalantly played the melody of "Falling in Love is Wonderful" on the conga drums, as you do. In fact the band were so nice that I probably cried again. It's not hard to find a reason for this shameless blubbing. Sonny Rollins is just about the last of his line: a swashbuckling, off-the-cuff improviser who personifies the very spirit of jazz. In many ways he's been an undervalued figure, not celebrated as a composer like Thelonious Monk, or as a bandleader like Miles Davis, or the founder of his own movement, like Charlie Parker. What Rollins really does is blow his horn, making any tune he chooses bow to his whim. Born in Harlem to parents from St Thomas in the Virgin Islands, his art exemplifies that fascination with ornament, and with insouciant showing-off, characteristic of migrant culture. He's suffered his share of racism, too. And I'll cry once again as I think about that.

The choice of songs was typically characterful from the man who once made "How Are Things in Glocca Morra" and "I'm An Old Cowhand" into vehicles for muscular improvisation. There was Noel Coward's "Some Day I'll Find You" (selected because – as Rollins told us in his broad, native New Yorker's accent – this was London), as well as a few of his own compositions including, of course, the iconic calypso "Don't Stop the Carnival".

This was played as an exultant encore with Rollins standing right at the stage's apron, pointing his sax down at the stalls and blasting the front rows with thunderous bass- notes, his feet dancing a cool little shuffle as he did so. Yes, I cried during that, too, thinking of Thomas Hardy's line about the passions of old age: "And shakes this fragile frame at eve, with stirrings of noontide". Then it was ovation-time as Sonny Rollins limped painfully off-stage and out of sight, helped by a Barbican minder. As the cheers continued, he came out of the wings for a brief moment to give us one final wave. And that was it, the show over by 9.15pm. It was enough, too: no one would have wanted him to work any harder. Truly, we will not see his like again. Let's hope that he returns next year.