When McCullum exited at 348, the pair had scored their runs in 52.5 overs at a run rate of 5.62.
The New Zealand captain struck his double century at a strike rate of 107.
Williamson, with a test career strike rate of 45, had inserted the wrong chip into his bat to make a test best 192 at his ODI cadence of 79.
It was reminiscent of Australia in the Steve Waugh-Ricky Ponting captaincy eras when they rattled along in excess of four runs per over to buy time for Shane Warne, Glenn McGrath et al to take the sort of rapid wickets which necessitated early hotel check outs.
McCullum stressed this was a "horses for courses" approach at the start of the series to make way for a second all-rounder.
Yet the captain has batted with such effect at No5 of late it seemed his more natural position to balance the team.
The spectacular result probably needs to be taken as an outlier given the extenuating circumstances of Australian batsman Phil Hughes' death which galvanised McCullum and Williamson into their laissez-faire approach. It was the equivalent of getting a business class upgrade for the hoi polloi; it can't be expected all the time.
No one wants to replicate the pall cast over this match by the Hughes' tragedy but it enabled the New Zealanders to release their inhibitions, particularly against spin. Suddenly they were 348 for one.
Even Daniel Vettori, now a 113-test sage who's not given to regular utterances of hyperbole, said: "I don't think I've seen anything like it", in reference to the partnership.
When the New Zealanders return to home conditions, the "horses for courses" strategy might again be applied by reverting to a more traditional opener to see off the shine with Tom Latham and allow McCullum to dominate a less frenetic ball lower down the order.
Still, good openers are hard to come by in New Zealand. Hamish Rutherford remains next in line as a member of the current squad. His return against Sri Lanka would also allow Corey Anderson to resume in what seems his more natural position at No6.
Alternatively, the selectors might accept the ups and downs of opening with McCullum and grant him an indefinite licence to let rip Sharjah-style.
Andrew Alderson travelled to the UAE courtesy of Emirates.