Defending champions Australia are the only team to have qualified for the semi-finals so far while New Zealand, India and England now occupy the other top-four slots.
New Zealand is still unbeaten in the World Cup and is sitting at the top of the Points Table with 11 points and five wins.
But New Zealand's wait to book that last-four spot must extend into their final two games against Australia and England.
And so Pakistani fans can barely stop themselves making comparisons with 1992 - their results in their first seven games of this tournament mirror those of the 1992 World Cup exactly, down to a washout in their third game, and the similarities have gone viral on WhatsApp.
Overnight rain delayed the start in Birmingham by an hour but the umpires decided the match would remain at 50 overs per side.
Thrashed by rivals India, crushed by West Indies and sunk by a collapse against Australia, Pakistan looked to be out of contention just days ago.
"We have got the momentum and I am confident that we'll win our remaining matches as well", Babar said.
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When Neesham pulled the final ball of the first innings into the Hollies Stand for six, it had actually capped a decent fightback from New Zealand, who sat a perilous 83 for five in the 27th over after winning the toss.
His opening bowling partner, Amir, has led the Pakistan attack brilliantly after being out of form for a couple of years after the 2017 Champions Trophy.
"We know we'd need to score runs off the pace bowlers".
Pakistan's batsman should realise that while New Zealand have comfortably chased down below par targets against Afghanistan and Sri Lanka, they have made it hard to chase down scores in excess of 240 against Bangladesh and South Africa. New Zealand's top wicket-taker was hostile and too quick for Imam-ul-Haq (19) and the chase was poised on a knife edge.
New Zealand´s Ross Taylor watches the ball after playing a shot.
Babar, however, said that team is not much thinking about what is being said about similarities with performance of 1992 world cup.
New Zealand: Kane Williamson (capt), Martin Guptill, Matt Henry, Tom Latham (wk), Colin Munro, Jimmy Neesham, Henry Nicholls, Mitchell Santner, Ish Sodhi, Trent Boult, Colin de Grandhomme, Lockie Ferguson, Tim Southee, Ross Taylor, Tom Blundell.