The opener smashed 126 from 135 balls in the hosts' final pool match at Hagley Oval today, helping her side rack up 265-8 against Pakistan.
Hannah Rowe then snared 5-55 to record the second-best figures of the tournament as New Zealand restricted their opponents to 194-9 and earned a 71-run victory.
But the win will almost certainly be insufficient to lift the White Ferns into the semifinals. They now need Bangladesh to upset England and South Africa to beat India tomorrow, with both results comprehensive enough to cause a big reversal in net run rate.
But Bates at least ensured the home fans that filled Hagley Oval - the first match at the tournament without a Covid-enforced crowd limit - would have walked away with smiles on their faces.
The 34-year-old became the first cricketer, male or female, to score centuries at four consecutive World Cups, having previously recorded tons at Australia 2009, India 2013 and England 2017.
Bates also crossed the 5000-run threshold in her 142nd one-day international, the fourth woman and first Kiwi to reach that figure, following Mithali Raj of India, Charlotte Edwards of England and Stafanie Taylor of the West Indies.
"I had no idea about the 5000-run mark," Bates told Sky Sport. "I don't follow the stats and the focus was on setting up a good score.
"But it is special and I'll probably reflect on it tonight, and I'm sure that there are some pretty big names in the 5000 club. It doesn't mean much at the moment but will a lot more with time."
The innings helped Bates put behind her what had been a largely forgettable World Cup with the bat. She also played a match-winning knock in the rain-affected win over Bangladesh, but failed to fire outside of two matches against the tournament minnows.
"It's been a tough tournament for the team and myself," Bates said. "Every day you want to turn up and play your role for the team but it hasn't worked out at this tournament.
"So it's nice to score some runs after having talked internally and with friends about how special it is to play for New Zealand."
Bates' innings also laid the base for her nation to build their highest total at this World Cup, overcoming the late-over struggles that had previously plagued their tournament.
After Pakistan won the toss and opted to bowl in Christchurch, skipper Sophie Devine fell for 12 in the sixth over, before Bates and Amelia Kerr put on 68 for the second wicket.
Bates also enjoyed decent partnerships with Maddy Green and Brooke Halliday, but the opener's dismissal in the 43rd over triggered another mini-collapse of 4-20 that threatened to once more wreck a solid platform.
Katey Martin, perhaps playing in her final ODI, ensured that wouldn't be the case, however, cracking an unbeaten 30 from 26 balls to help New Zealand complete their 50 overs for the second time at the tournament.
"I thought 250 would be a good score and anything above would be handy," Bates said. "I wanted to bat with Katey but couldn't. It was great to see her finish the innings, which was a team goal all this tournament."
In reply, Pakistan never lifted their run rate to a competitive level, seemingly content to occupy the crease.
Spin pair Frankie Mackay (2-29) and Amelia Kerr (1-36) played a significant part in their opponents' slow scoring, completing fine tournaments with the ball.
Rowe then returned for a second spell in which she picked up all five wickets, while Amy Satterthwaite - another veteran nearing the finish line - was given the honour of bowling the final over as the White Ferns' tournament came to a likely close.
