As a capacity crowd roared at Smoothie King Center in New Orleans, Glenn Robinson III, blank-faced, put his right index finger to his lips.

It was February 2017, and Robinson — the Pacers’ backup small forward — had leaped over the 6-foot-9 Paul George, the team mascot and a cheerleader before throwing down a reverse dunk to win the NBA Slam Dunk Contest. A relative unknown, Robinson edged Derrick Jones Jr., DeAndre Jordan and Aaron Gordon, showing a national TV audience that he’s more than just the son of former All-Star Glenn Robinson.

“I’ve been an underdog all my life, all my career,” Robinson said when he accepted his trophy. “This is just the beginning for me.”

More than two years later, that dunk contest remains the high point of a career plagued by injuries and inconsistency. After the Pistons declined Robinson’s $4.3 million team option for next season, he agreed to a two-year, veteran-minimum contract Tuesday with the Warriors, with a player option on the second year.

This is a marriage rooted in mutual need. With no salary-cap room, Kevin Durant and Andre Iguodala gone, and Klay Thompson expected to miss at least the first couple of months of next season with an ACL injury, the Warriors eyed a cheap wing who can defend multiple positions and knock down 3-pointers. Meanwhile, Robinson wanted to resuscitate his market value after a disappointing season with the Pistons.

With Golden State, he’ll get plenty of opportunity to prove that he’s still the “3-and-D” wing who once thrived as George’s primary backup with the Pacers. Alfonzo McKinnie, who carved out a rotation spot last season after making the Warriors in training camp, is the only true small forward other than Robinson on the 2019-20 roster.

Assuming Golden State doesn’t trade guard D’Angelo Russell, it will probably start Thompson — almost exclusively a shooting guard his entire career — at small forward when he returns from his knee injury. But with Thompson sidelined until at least early December, Robinson and McKinnie will shore up the position, taking turns on opponents’ top scorers.

The loss of Durant and Iguodala leaves Thompson, when healthy, and Draymond Green as the Warriors’ only proven perimeter defenders. Robinson and McKinnie both boast the length and athleticism to become above-average defenders, but they’ve been inconsistent.

Too often, Robinson appears overmatched against bigger forwards, getting bullied both on the perimeter and inside. His effort on the defensive glass has also been problematic. The Warriors hope Robinson can build off his second half of last season, when he posted a defensive rating of 99.1 in limited minutes over the final three-plus months. That would have ranked tops among the Warriors, none of whom had a defensive rating better than 104.3 last season.

Perhaps nothing will determine Robinson’s success next season more, however, than his ability to hit open shots. With Quinn Cook gone, the Warriors need another floor spacer — especially while Thompson is out. Robinson, who converted over 38% of his shots from behind the arc from 2014-15 to 2017-18, is capable of filling that void.

But first he’ll need to cure whatever ailed him last season. After missing most of 2017-18 with a severely sprained left ankle, Robinson struggled to find a rhythm with the Pistons, shooting 29% from 3-point range.

Detroit’s 105.5 offensive rating with Robinson on the court last season was a far cry from its 110.3 rating without him. Outside of the occasional highlight-caliber dunk, he was largely a liability on that side of the ball. This was a big reason why Robinson’s minutes plummeted after he returned from an ankle injury in late December.

Few were surprised when the Pistons declined their team option on Robinson for next season. In high-pressure situations, Detroit head coach Dwane Casey was more comfortable with Reggie Bullock, Bruce Brown, Langston Galloway, Luke Kennard and Stanley Johnson as his rotation wings.

Still, the Warriors view Robinson as a worthy reclamation project. Those close to him rave about his work ethic and easygoing personality. At age 25 with a 44-inch vertical leap and a 6-foot-10 wingspan, Robinson still has considerable upside, at least as a backup wing.

Career stats After averaging 12 points per game in two seasons at Michigan, Glenn Robinson III has spent the past five seasons in the NBA, playing for three different teams. His career stats: Games219 Average minutes14.4 Average points4.4 Average rebounds2.1 Average assists0.6 Field-goal percentage43.9 3-point percentage36.1

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Golden State is banking that Robinson can avoid the fate of Jeremy Evans, Fred Jones and Isaiah Rider, freak athletes whose NBA careers topped out at the Slam Dunk Contest.

Connor Letourneau is a San Francisco Chronicle staff writer. Email: cletourneau@sfchronicle.com Twitter: @Con_Chron