New Zealand are without regular skipper Kane Williamson, who is set to miss the 50-overs World Cup in India later this year with a knee injury, while several others are playing in the Indian Premier League.
Staring at a series defeat after back-to-back losses, the touring side put up a competitive 163-5 at Lahore's Gaddafi Stadium on Monday on the back of Tom Latham's 49-ball 64.
Pakistan slumped to 88-7 in reply but Iftikhar Ahmed's 24-ball 60 injected drama into the contest.
Pakistan needed five runs off the last three balls but Jimmy Neesham removed Iftikhar, followed that with a dot ball, and then dismissed Haris Rauf to thwart the hosts.
"It was obviously a hell of a game of cricket and awesome for the boys to get across the line," Mitchell, who made 33, said on Tuesday.
"It gives the guys a lot of confidence heading into the rest of the series and you never know what will happen over the next few games."
Mitchell was proud how New Zealand had fought their way back into the series but said they would need to adapt quickly in Rawalpindi, which hosts the last two matches on Thursday and next Monday.
"It's obviously a new ground, a new challenge and a new surface. So we'll be pretty clear on how we want to play on that surface.
"We'll adapt as quickly as we can. Hopefully we win a few little moments and we'll see what happens."
