The Warriors won 30-26 on Saturday in Brisbane after leading 30-12 with 25 minutes to play, victory their sixth in seven games to push them to an equal-best start in club history at 6-2.
The Cowboys scored three tries in seven minutes - they had a fourth denied two minutes later - and seemed destined to surge home on a wet night at Suncorp Stadium in front of 49,512 fans.
But halfback Luke Metcalf, who had dominated with two tries and two line breaks in the first half, came up with the try-saving tackle on a flying Murray Taulagi that halted momentum and the Warriors hung on.
"Emotions are, I need a heart transplant," the Warriors coach said.
"But proud, hung in there (after) making it so hard for ourselves when the Cows were so good in the second half."
Former Cronulla playmaker Metcalf's first-half clinic had the Warriors on track for a cruisy win, the halfback scoring twice and running for 111 metres.
Halves partner Chanel Harris-Tavita was equally as damaging with two try assists and a four-pointer of his own, before Adam Pompey's 80m intercept try from a regrettable Jake Clifford pass made it 28-12 at the break.
Three Cowboys tries got them back within a score with 18 minutes still to play, Taulagi contorting himself superbly to score the second and Jeremiah Nanai producing a huge hit to spark his side.
But Metcalf, flourishing in the shadows of Shaun Johnson's retirement, delivered in defence, the 6-2 record only matched by their 2018 start as the best since their 1995 inception.
"I think he's proved that (he can manage a game) now and it's time to play a bit of footy," Webster said.
"And halfback's aren't renowned for that (defence), but good ones are."
The Warriors will move up to third at worst once the festivities conclude in Brisbane on Sunday.
That's despite their off-colour start in a poor loss to Canberra in Las Vegas's opening round and Johnson's exit after a 13th-placed finish last season left a gaping hole to fill.
"Our DNA's starting to show," captain Mitch Barnett said.
"We're not where our ceiling is. If we can learn while we're winning, especially those tight ones, at the back end we'll be so much better for it."
Cowboys coach Todd Payten was happy to praise the Warriors as a "top-four team".
"It's hard to win lots of them, like they have," he said.
"They're a gritty team, direct and confrontational … and have a young, developing spine with great upside.
"You can't give a good team that much of a head start.
"Very proud, but very disappointed not to ice those last couple of sets. They found a way to stop us."
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