The league Golden Boot leader boosted his tally a few minutes later, following up to score after Waitakere United goalkeeper Danny Robinson had saved an initial Luis Corrales effort.
The home side were handed a lifeline on the half hour mark as Peverley turned a Tom Shaw free kick into his own net but Team Wellington's two-goal edge was restored before halftime when Harris completed his hat-trick, finishing off Tom Jackson's cross 36 minutes in.
Waitakere missed an opportunity to reduce the deficit two minutes before halftime as Butler struck a 43rd minute penalty against the upright after Alex Feneridis had fouled Ryan Cain in the area after a corner.
That moment may have proved decisive as the visitors cruised to victory in the second half, rarely troubled by Waitakere and Peverley converted from the spot to make it 4-1 just before the hour mark after Andy Bevin was felled in the area by Aaron Scott.
The hosts did manage a late consolation goal via Lovemore's tidy flicked finish from close range but it was never enough on the night which saw their skipper bring up his historic milestone.
Calcott was content with his team's effort which puts the remaining teams in the hunt for the playoff spots under a bit of extra heat ahead of the weekend's remaining Round 12 fixtures.
"We're delighted to get the three points because that's our fifth game in 17 days," Calcott said.
"It was a good start and that gave us a platform to kick on in the second half. Obviously we're not too happy about the two soft goals but really happy with some of the football we played and it puts a bit of pressure on the other teams now with the Thursday night win.
"What I'm really happy about is we're getting stronger and stronger week to week and showed that tonight and we've showed it the last couple of weeks."
Butler, who plans to keep playing as long as he can, reflected on a terrific personal milestone tinged with the disappointed of not being able to mark it with a victory.
"It's a good night for me, it's nice to be recognised for 200 games. I've had heaps of messages and it's really quite humbling the response I've gotten," the Waitakere skipper said.
"It's a bit of a shame, that first half performance was pretty bad to be honest. We didn't give up, we kept fighting but defensive lapses cost us again.
"We're good for 10 minutes and bad for 10. This league is too good to be like that. Every time we have the bad patch we get punished. It's the sign of a good league."
"I'll keep playing until I can't. I need to learn how to take a penalty though, that was terrible."
