“I just turned 68 years old,” says Carlos Santana, “and, as you can see, I’m still relevant.” There’s a breathy intonation on the word “relevant”, as if he’s slightly abashed to find himself one of the last of the Woodstock generation to be still fit and powering through two-hour shows. A sold-out O2 and recent platinum album – 2014’s primarily Spanish-language Corazón sold 2m copies in the US – confirm that the appetite for his Latin-jazz-rock fusioneering has never dimmed, even if he’s had to consort with Pitbull (who rapped on Corazón) to get a foot in the door with younger listeners.

If anything, tonight’s Latin-funk set sounds defiantly contemporary: what was once esoteric – Woodstock was Santana’s breakthrough precisely because they were so different from the guitar bands on the bill – is now part of a pop terrain in which bachata and cumbia coexist alongside pop and R&B. Santana’s show is a street party incorporating all of the above, as well as snippets of showboating: the Mexican-American guitarist can’t let his only UK gig pass without throwing in London Bridge Is Falling Down.

A career’s worth of music is dealt with here, recreated by a 10-piece band that includes two singers – Carlos himself only sings a few choruses and implores us to “see beyond religion” and love each other. The opening Soul Sacrifice, from 1969, gets its full 10 rumbustious minutes, and leads into a breathless 2003 Brazilian dancehall cover, Saideira. The 1999 album Supernatural gets a good going-over, with Corazón Espinado’s burning salsa giving way to that decade’s most inescapable Latin-pop hybrid, Smooth.

The guitarist is physically unobtrusive, but his sound is inimitable, cutting through the horns and percussion. It’s not so much a gig as a joyous jigsaw of party tunes. Thirty seconds after leaving the stage, they’re back for an encore of Black Magic Woman and Oye Como Va, disinclined to let the evening end.