Van't Schip revealed that a shift in training focus had proven pivotal, particularly after last week's 4-1 loss to Adelaide United.
"We trained very precise and secure towards this game - we changed the formation a bit because looking at our last games, some parts were good but we also looked a little bit vulnerable," he said.
"We tried to change a few things, and that paid off with the result today."
Van't Schip said getting marquee man Robert Koren into position with Erik Paartalu and Aaron Mooy behind him had been key.
"We've played like that before, so it's not something new.
"And players are now in better physical condition, compared to a few weeks or months ago."
Players like David Williams, Harry Novillo and Josh Kennedy were finding the sort of form which could threaten against Victory on Friday.
Van't Schip said his players would need to lift again, but he was confident they could.
"There's still a lot of things we can improve, but I think we looked solid. We were dangerous going forward and very hard to beat defensively."
After a scoreless first half, Wellington started the second spell brightly but City gradually worked its way back into the game.
Goalscorer Kennedy was low-key about his effort afterwards, saying it was just a matter of being in the right place at the right time.
"I had a few good chances before, especially with that header, so it was probably sort of building," he said.
"I felt it was getting closer and closer, those two crosses from Jonny were brilliant.
"After we got that 1-0 I thought we did well and then we got the second, and the game changed.
"We probably got ourselves in a bit more trouble than we should have sitting back too deep but the boys at the back did extremely well."
