Chasing 238 on a tricky Edgbaston pitch which offered vicious turn, Azam (101) and Sohail (68) showed intent, temperament and resolve while batting in Pakistan's must-win game.
They raised a 126-run stand for the fourth wicket after Mohammed Hafeez's dismissal off a part-time spinner, yet again, raised eyebrows and Mitchell Santner looked almost unplayable.
The situation demanded restraint and Hafeez was set but he threw away his wicket while trying to attack Kane Williamson.
This was after Fakhar Zaman (9) was done in by Trent Boult and Imam ul Haq (19) became a victim of Lockie Ferguson.
Taking the attack by the scruff of its neck, Azam shifted the gears after completing his half-century and hit some glorious shots off Williamson and Boult to keep the required run-rate under check.
The 24-year-old completed his century, 10th in ODIs, with a single of Lockie Ferguson off. His knock, coming off 127 balls, was embellished with 11 shots to the fence.
Sohail provided superb support from the other end before running himself out. Only two runs were required at that time. Williamson tried all the tricks in his bag but Pakistan overhauled the target with five balls to spare.
With this win, Pakistan have now moved up to number six in the table with seven points from as many games. They now need to win their last two games against Afghanistan (June 29) and Bangladesh (July 5) to hope for semifinal qualification.
The win-lose sequence in first seven matches for Pakistan is exactly the same what they had in their victorious campaign in the 1992 World Cup.
New Zealand, who lost their first game of the tournament, stayed on number two with 11 points, behind Australia (12).
Earlier, New Zealand’s Jimmy Neesham finished with a gutsy career-best 97* when it really mattered for his team to propel New Zealand to a defendable 237/6 from 50 overs at Edgbaston . Pakistan speedster Shaheen Afridi yet again proved why he loves playing against the Kiwi’s as he bowled a fiery spell along with Aamir to reduced New Zealand to 83 for five. Afridi rattling the Kiwi batsmen is no surprise as he averages just 10.83 against them with the ball in ODI cricket.
Nothing seem to work for Pakistan after that with Neesham and de Grandhomme building the innings bit by bit. They worked the ball around, stayed patient until it was time to accelerate and finally managed to help their squad put on a defendable total on the board.