Needing a victory in their final group match to avoid the nightmare scenario of potential elimination, England rose to the occasion to reach the World Cup semis for the first time since 1992.
England captain Morgan felt the turning point came when his openers Bairstow and Roy piled on 123 for the first wicket, laying the foundations for their 305-8.
Bairstow top-scored with 106 from 99 balls and Roy added 60 before New Zealand were bowled out for 186.
“I thought we were outstanding today. It started with the two boys at the top of the order. They set a good solid platform playing in the manner they do. Jonny getting his hundred was match-winning,” Morgan said.
“The wicket did change after the 25th over and it did slow up. It was difficult to score. Every batsman found that so to have so many on the board was encouraging. It was about trying to get as close to 300 as possible.”
After losing to Australia at Lord’s, England were in danger of failing to finish in the top four of the 10-team group phase but composed performances against India and New Zealand have restored belief they can win the tournament for the first time.
Morgan believes rediscovering the aggressive, confident style that marked their rise up the one-day international rankings has sparked their revival in the nick of time.
“The manner in which we have played in the last two games is the identity we have been playing with for the last four years,” Morgan said.
“Playing with freedom and intent with the bat and had bowlers looking to take wickets throughout the 50 overs with the ball. Hopefully we can produce that aggressive, positive identity in the semi-finals.”
New Zealand are still likely to qualify for the semi-finals barring a huge victory for Pakistan against Bangladesh on Friday.
Black Caps skipper Kane Williamson conceded his side were out-classed by England and need to improve.
“Full credit to the way England played today. We definitely need to be better moving forward,” Williamson said. “England did get the best of the conditions but they were the better team. They outplayed us in all facets.
“Going ahead, touch wood, hopefully it all works out and we are in the semi-final but in some ways, it starts again. We haven’t played our best cricket yet.”