But there were no shortcomings here at Edgbaston on Wednesday as Shaheen hit the right areas to bring New Zealand to their knees in a marathon seven-over spell.
Their non-selection of legspinner Ish Sodhi was an increasing talking point as Pakistan raced to victory.
This was after Fakhar Zaman (9) was done in by Trent Boult and Imam-ul-Haq (19) became a victim of Lockie Ferguson.
NZ captain Kane Williamson said the Black Caps had a chance with early wickets, but they could not make a breakthrough against Azam and Sohail. Hindsight is a wonderful thing, but it was a bad misread of a previously covered pitch, a safe option for an unbeaten team. In my view, Pakistan's inability to find their best playing 11 has hurt them quite badly throughout this tournament. "We are top on the list of teams dropping most catches in the World Cup which isn't a good sign", Akram said.
New Zealand, on the other hand, have been invincible so far and now hold the top position in the points table.
But Babar transcended these conditions, overcoming the pace of Lockie Ferguson, the swing of Trent Boult and some considerable turn for Mitchell Santner's left-armers with a frictionless innings of 127 balls and 11 fours via some delightful cover drives. Williamson waited until the 24th over to bring himself on and struck quickly thanks to an bad Mohammad Hafeez shot.
"The team, other people are standing up at different times, and you can back everyone to do a job rather than just relying on a couple of key players".
The superstitious may note the similarities to 1992 - where New Zealand's unbeaten run was ended by Pakistan, leading to an eventual semifinal exit against the same foe.
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Suddenly the horse had bolted as Sohail backed up his matchwinning knock against South Africa and Babar's positive intent and brutal dispatch of the loose delivery paid off.
Reduced to 83 for five after electing to bat, New Zealand looked up to Williamson for yet another rescue act but it was Neesham and de Grandhomme, who revived the Kiwi innings with their 132-run partnership.
Following a delayed start due to a wet outfield, following heavy overnight rain, Kane Williamson's decision to bat first on the used pitch quickly looked like a poor one as Mohammad Amir bowled Martin Guptill (5) with his first ball, via an inside edge.
Matin Guptill chops on from Mohammad Amir for another low score at this World Cup.
The combo of Sarfaraz and Afridi was at it again and this time Tom Latham (1) was consumed.
Pakistan's batting line-up has been vulnerable and given the top class performance of New Zealand's bowlers, Pakistan will have to be careful against them.
Neesham and de Grandhomme are there as batting finishers, to launch from a solid platform. With Shaheen on fire, New Zealand lost three wickets in a span of 22 runs.
Destiny remains in their own hands and they will not want their white-ball journey under the management of Trevor Bayliss and Morgan to end in Chester-le-Street, the scene of its glorious beginnings when they edged home in a thrilling series decider against the Black Caps four years ago.