Here’s a puzzle: You’re a credit card company — with a reputation for serving the wealthy — rolling out a new program that enables your cardholders to earn discounts and perks for tweeting about the purchases that they’re about to make. How do you promote this new program that rewards people for something that seems a lot like conspicuous consumption?

By hiring the guy who brought the phrase “big pimpin’ / spendin’ cheese” into the national lexicon to perform an exclusive concert for a small selection of your cardholders who work in the tech industry and attended SXSW Interactive, naturally.

And thus did Jay-Z descend upon SXSW, sponsored by American Express, to promote the new Amex Sync program.

Though he strolled onto the stage of the Moody Theater at ACL Live 36 minutes late (he needed a police escort to get to the venue from the airport), nobody much seemed to care – the mere fact that they were all in the presence of Jay-Z, for free, on a Monday night, seemed to be enough for the assembled techies. The fact that Jay’s set was a straight-up greatest hits performance helped, too – entering to the sample of Russell Crowe from Gladiator shouting “Are you not entertained?!” that opens “What More Can I Say?”, he delivered almost exactly what an audience could want from a Jay-Z show for 75 minutes. (Almost – there was a weird excursion into Kingdom Come’s much-maligned Coldplay collaboration “Beach Chair” toward the end of the set that stole some momentum from the room.)

Still, who cares about that? Jay was in total control of the 2,700-person room, calm and smooth and clearly having fun from the first moment, shouting out SXSW and happy to be there. Backed by a semi-live band — a drummer, two keyboards, and a sampler/DJ who sometimes made the other three irrelevant –—Jay seemed downright triumphant. This was a crowd that belonged to him, for sure.

It wasn’t just the hits, either — though that helped. Jay-Z has never topped lists of “great live performers,” but on Monday night, he seemed as though he ought to: his delivery was punctual and unhurried for an hour-plus, his energy was high, and he owned the crowd throughout the night. When his daughter, Blue Ivy™, was born in January, reports were that Jay would no longer be using the word “bitch” in his lyrics. Though he later clarified that he hadn’t said that, it wasn’t an issue at ACL Live during “99 Problems” — all he had to do was turn the mic toward the crowd after uttering the words, “If you’re having girl problems / I feel bad for you son,” and the audience would ecstatically shout the rest.

During “Run This Town,” the emcee was surprisingly insistent that the audience deliver the Rhianna parts; in “Heart Of The City,” from 2001’s The Blueprint, Jay ended the song by insisting that he crowd repeat the Bobby “Blue” Bland sample that outros the tune three times — 2,700 voices warbling, “Ain’t no love / in the heart of the city / ain’t no love / in the heart of toooooown” as one at his behest, a power that few but Jay-Z possess.

There was audience participation, there were hits (“I got a million of these,” he boasted, seemingly only a slight exaggeration as he played radio staple after radio staple), and there was showing off, as Jay frequently silenced his band to drop verses a capella. There was a lot of excitement, as the audience — mostly from New York, if the cheers when Jay asked where everyone was from during “Empire State Of Mind” were any indication — realized just how intimate ACL Live is as a venue, and, by extension, how close they were to Jay-Z himself.

There were occasional surprises — like the down-tempo, introspective “Beach Chair” — and a shout-out to parents (“the first one,” Jay explained) before “Glory,” the song he penned to pay tribute to the joys of new fatherhood. There was a coda of massive hits — “Hard Knock Life,” followed by “Empire State Of Mind” — and then an encore (“Encore”), followed by a capacity crowd still chanting “Ho-Va! Ho-Va!”

In short, there was plenty of love in the heart of the city from a bunch of Twittering Amex cardholders, and it never even seemed that weird.