Aziz Ansari, Soho Theatre, London

A superstar in the making – even if he does shoot puppies

The roll call of Indian American comics doesn't exactly trip off the tongue, but in the past few years a new generation of talent has emerged on US television, from the scene-stealing Danny Pudi in Community to the tongue-tied Kunnal Nayyar in The Big Bang Theory via Iqbal Theba's Principal Figgins in Glee and Mindy Kaling's Kelly Kapoor in the US version of The Office.

But perhaps the most talented of the bunch is Aziz Ansari.

Though not yet a name here (not that you'd know it from the speed with which this five-date tour sold out), he has made a splash Stateside with bit-parts in Flight of the Conchords and Scrubs, followed by a breakthrough role in the NBC hit Parks and Recreation, and a film-stealing turn as the hilariously awful, loudmouth comic Randy in Judd Apatow's movie Funny People. Being a loudmouth, however, is anathema to Ansari's own act; dressed like a latter-day member of the Rat Pack, he is charm personified, making it clear that being the host of last year's MTV Video Music Awards isn't about to go to his head.

Ansari's act, like that of his excellent warm-up Dan Levy, is not blow-you-away stuff – he runs through the familiar gamut of the difficulties of approaching a woman at a bar, wasting hours researching inane subjects on the internet, and the hazards of predictive texting – but it is solidly funny and slickly executed, and he throws in more than enough unexpected payoffs (not the least of which involves the shooting of puppies in the face to teach a couple a lesson in respecting the elderly).

He also treads the precarious line of racism with precision, exploring his favourite ethical slurs ("a touch of the tarbrush") and revealing how it is possible to make almost any word or phrase seem racist just through its enunciation. His chosen phrase for the evening is Kit Kat – "Brown on the outside, wafer on the inside". No, it doesn't make sense, but then, nor do racist epithets.

His delivery is never less than at devastatingly breakneck pace as he veers from stories about the absurdity of his cousin's university application form (a free-form essay that equated the atomic bomb with DVDs at check-out counters) to the rapper 50 Cent's astounding lack of fruit awareness.

But by far the biggest crowd-pleasers come during his encore, for which he digs up an old Randy routine ("I can't believe how stupid those jokes are"), ruminates on the similarities between buying bed sheets and drugs, and sounds off on his pet subject, R Kelly, with the suggestion that the rapper start putting together his own dictionary: "Vegeburger – like when a cheeseburger tastes weird."

The set has a beautiful flow to it, and Ansari's affability (apparent also in his willingness to pose for photographs afterwards), timing and quick wit bode well. When he returns to these shores, don't be surprised if this budding superstar is playing rather larger venues.