McCullum's unbeaten 59 off 45 balls kept New Zealand afloat but half centuries from Kamran Akmal and captain Mohammad Hafeez set up a win off the penultimate ball.
"The result wasn't as ideal as we would have liked but it was a good hitout in a competitive environment," seamer Tim Southee said.
"The idea is to try things out before the tournament in conditions we're going to be faced with. We gained a lot out of it, leading into the Australia game."
Pakistan possess two T20 bowling aces. Seamer Umar Gul is an old hand at the skills required in the shortest game. Twice he's taken five for six - including against New Zealand at The Oval in 2009 - and only Sri Lankan spinner Ajantha Mendis has done better.
Offspinner Saeed Ajmal had the New Zealand batsmen in knots. To be fair, he has plenty of previous for that.
Southee, and spinners Nathan McCullum and Ronnie Hira, were tidy, but didn't have enough runs to work with.
The experiment with Kane Williamson opening didn't work, but won't be discarded immediately.
The format against Australia is interesting. The day's activities will start an hour earlier than scheduled - but won't be televised - and will consist of a T20 game, followed by a five-over game and a Super Over shootout. Both teams should get much out of the day.
There is a feeling this will be a tournament full of relatively low scores unless the pitches are sparked up between now and the beginning of the tournament proper early on Saturday. The odds on that are as low as some of the deliveries at the Shere Bangla Stadium yesterday.
"140 is very defendable on these wickets. With their slow nature it's hard [for batsmen] to get yourself in," Southee added.
In a form of the game where totals approaching 200 are becoming more common, this could yet turn out to be a bowler's tournament.
What's next
* New Zealand play Australia in their second and final warm-up game for the World T20 in Fatullah tonight.
* They will play a T20 game, followed by a five-over contest and a Super Over.
* New Zealand's first group game is against England in Chittagong early on Sunday morning (NZT).