Hans Zimmer wanders alone on to a cluttered stage, sits at an electric piano and tinkles out the frail melody to a speakeasy rag from Driving Miss Daisy. He’s joined by a puckish clarinet player echoing his top line, then a ragtag family of musicians gathers; a trio of strident strings in party frocks, longhair electric guitarists, indie banjo players, a wild west villain with an accordion and a jigging violinist in a deerstalker whom Zimmer, he’ll later explain, stole from Ennio Morricone. As the piece merges into the Balkan disco segment of Madagascar, curtains lift to reveal a full orchestra and stage-wide choir, here to help Zimmer build empires, explore universes, bring woodland chases to sticky ends and total Batmobiles.

Joining a mere handful of arena-filling soundtrack composers, this German-born Hollywood legend might not have the opening credit hits of Morricone or John Williams, but his roots in punk and new wave – he worked with the Damned and the Buggles at the start of his career – have furnished him with the nous and showmanship to construct a show that’s as much gig as recital. More rock star than conductor, he wanders the front of the stage playing guitars, synthesisers and percussion and reminiscing wittily about these prime cuts from his 150 soundtracks, although he stops short of his theme tune to Going for Gold or anything from Batman v Superman, perhaps in case anyone who has seen it suffers post-traumatic flashbacks.

A master of marrying bombast, tension and delicacy, each of Zimmer’s scores naturally evokes its parent picture. Crimson Tide bristles with espionage, as brooding and powerful as a nuclear submarine. Gladiator drifts from ancient military march to orgiastic bacchanal, featuring gorgeous vocal hooks from singer Czarina Russell and Zimmer plucking at a classical guitar as the fury of a vengeful Maximus Decimus Meridius builds at his back. There’s a savannah’s scope and grandeur to The Lion King; The Dark Knight’s staccato stabs and night-skulking horns come at you like a Gotham vigilante, and Interstellar blasts off into new dimensions of gargantuan orchestration, hitting a celestial high.

There’s real variety, too; the band don admiral hats and shoulder parrots
for the momentous Romany swing of Pirates of the Caribbean, become a Rammstein rock outfit for Electro from The Amazing Spider-Man 2 and summon haunting atmospherics on Aurora, a piece written to “throw our arms around the loved ones” of the victims of the Aurora, Colorado cinema shooting in 2012. With the Smiths’ Johnny Marr on spectral guitar, a swelling Inception closes a wonderful night that feels like being caught in a whirlwind of interlocking dreams.

• At SSE Arena, Wembley, 7 April. At Barclaycard Arena, Birmingham, 12 April.