SAN ANTONIO — This was a major test for the Warriors.

Maybe the biggest test of the season. There will be sterner tests to come, for sure, because the top teams in the playoffs seem to be relishing their shot at the kings of basketball. But this was a character check, and the Warriors aced it.

“To be playing as bad as we’ve been playing, and to get to where we need to be, is big,” Warriors forward Draymond Green said.

Despite the doubts and worries that piled up over the last month of the season, the Warriors showed Thursday night that the magic is still there: Dubs gonna Dub.

It wasn’t a happy or joyful win, the Warriors’ 110-97 beatdown of the Spurs, for a 3-0 series lead, but it was ruthlessly businesslike, on a night when danger lurked.

Steve Kerr, almost always the smiling and gracious head coach after games, win or lose (mostly win), walked sadly off the court when this one was over, directly to the locker room. His good friend, San Antonio head coach Gregg Popovich, was suffering the loss of his wife — and Kerr was suffering along with him.

Guaranteed, Kerr did not celebrate this win, unless it was to sip a glass of wine to silently honor Popovich and his wife Erin, who once exiled her husband in the doghouse when he traded a fringe bench player named Steve Kerr.

But basketball was advertised, and basketball was played, and the Warriors did their job on a night when they could have fallen into about a dozen traps.

“It was a perfect setup for a letdown,” Green said, adding, “and I don’t say that to be insensitive. A game doesn’t matter.”

But a game was played, and there were traps for the Warriors.

•Teams up 2-0 in a series, especially in the first round, often experience some letdown.

•The Spurs were a desperate team, on their home court, where so many Warriors’ dreams over the years have been trampled. And the Spurs were able to dictate the early pace, take the wind out of the Warriors’ sails.

•The Spurs, whether or not they stated it, were playing this one for their head coach, and in honor of his wife. Not necessarily to win, but to show the heart that the Popoviches exemplify to this team and this town.

Fortunately for the dignity of the game, nobody played the card of winning one for the Popoviches. Death is bigger than any stupid basketball game; tragedy should never be used as a handy motivational tool. The death of Erin Popovich was something that nobody could ignore, but was treated respectfully.

Gregg Popovich, who was not at the arena, except in spirit, would not have had it any other way.

It was just a basketball game, but for the Warriors, it was an important one. They showed that they had the mettle to muddle their way through a dangerous puddle. To bring their game.

The Spurs opened with Rudy Gay posterizing JaVale McGee on a driving power-slam, followed by Patty Mills stealing the ball from Kevin Durant and scoring.

The Spurs might be in the waning days of their two-decade dynasty, but they weren’t going to roll over in this game, and the Warriors knew it, and responded.

And it was an ensemble job on offense, contributions all around, but it was the Warriors’ bedrock defense that held down the fort (not the Alamo) when their three-point shots weren’t falling and the Spurs were coming hard.

And it was Green who sparked that defense. He had one of his jackhammer games, busting up one offensive play after another — switching on some plays, staying home on others, disrupting a San Antonio offense that, when it gets going, can be efficient beyond the sum of its overmatched parts.

“Our defense, just consistently over the game, was the difference,” Kerr said.

Green had four blocks, most since the All-Star break, and Kerr said, “He’s been fantastic, defensively. He’s been all over the place. This is a team that you have to disrupt. They’re excellent with their execution ... and Draymond is as good as anybody I’ve ever seen in terms of recognizing a play and blowing it up.”

In some ways, the game took on an almost boring predictability, the Spurs fighting gamely but simply getting worn down and outplayed by a team with superior talent.

On paper, it might look like a decent performance by the team that went into the playoffs favored to win it all, merely a routine tuneup before the real action begins in the second round.

But it was more than that for the Warriors. It was a statement, to the world and to their fans. And to themselves.

Scott Ostler is a San Francisco Chronicle columnist. Email: sostler@sfchronicle.com Twitter: @scottostler