For head coach Jones, who guided his players through two testing weeks in South Africa to open the United Rugby Championship season, this first win was about making a statement in their adopted home.
“I am very happy,” said Jones, his satisfaction clear after the final whistle.
“When you get your first home game, especially in your new home or temporary home for this season, you want to get off to a good start.
“You only get one chance to make a first impression and I thought in all areas of our game today, we showed high quality.
“I suppose the only maybe slight down is we didn't get the five points but to have a zero next to your name is good.
“We spoke about improving our defensive performance and continuing with the good attack stuff. I think we made another step forward in all those areas, which is why I'm very happy for the players.”
The Ospreys’ decision to relocate to Bridgend for this season — while St Helen’s in Swansea undergoes redevelopment — is a practical one.
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But the Brewery Field has been a happy hunting ground in recent years, hosting memorable victories over the DHL Stormers, Sale, Cardiff, and Edinburgh.
Now, it will serve as the beating heart of their campaign, and Saturday’s dominant display was the perfect way to introduce themselves to a crowd of 4,519.
It was a performance built on grit and precision. Tries from Phil Cokanasiga, Morgan Morse, and James Ratti, along with nine points from young fly-half Dan Edwards, sealed a commanding win and snapped a run of four straight league defeats stretching back to last season.
Zebre, buoyed by early-season victories over Edinburgh and the Lions, were outclassed from the start.
Their attack rarely threatened, and their defence buckled under sustained pressure from the Ospreys pack.
The Italians have now won just twice in 41 league matches on Welsh soil.
For Jones, the performance was the culmination of lessons learned abroad.
The Ospreys had shown promise on their South African tour but came home with just a single point to show for their efforts.
“We worked really hard in South Africa and were pretty gutted only to come away with one point from the two games,” said full-back Jack Walsh.
“So it’s really good to get a win. The support was awesome. It’s massive for us.”
That support, and the intimacy of the Brewery Field, was something the players fed off throughout the evening.
Second row James Ratti — one of the try scorers — believes the venue is fast becoming a fortress.
“We showed that teams who come to the Brewery this year are in for a contest,” he said.
“The atmosphere was great. It’s becoming a little mini cauldron for us, with the fans right on top of us. It’s always a good experience playing here.”
It was an especially proud night for captain Dewi Lake, leading his side in the absence of injured Wales skipper Jac Morgan.
Born and raised in Bridgend, Lake has deep roots in the area and relished the opportunity to wear the armband in front of a home crowd.
“I grew up here, and I love playing here,” he said.
“We have had some very memorable wins here over the last couple of years, and this one certainly goes up there, to nil a team like Zebre, who had started the season as quickly as they had. It’s excellent for us.”
The 24-0 scoreline flattered Zebre in truth; the Ospreys could easily have claimed the bonus point.
But the clean sheet — their first since April — was a source of particular pride for Jones, who has been emphasising defensive resilience since taking over.