LOS ANGELES — Steve Ballmer, the former Microsoft executive, has spent billions to transform the Los Angeles Clippers. He paid a record price to become owner in 2014, swung deals for superstars, conceived a new arena and upgraded the organization’s facilities, front office and coaching staff.

But resolve is a quality that can’t be bartered or bought, and unfortunately it’s one that has eluded the Clippers throughout their history. Los Angeles entered its NBA first-round playoff series against the Dallas Mavericks with the edge in superstar talent, experience, depth and shooting, plus home-court advantage. Then it promptly lost the first two games at Staples Center, fell behind by 19 points in Game 3 and appeared to have no reliable defensive solution for Mavericks star Luka Doncic. Deja vu didn’t begin to describe the Clippers’ predicament; confounding collapses, such as blowing a 3-1 lead in a second-round series against the Denver Nuggets in the bubble last year, have been the rule, not the exception.

Make no mistake: The Clippers nearly endured another round of heartburn, with forward Nicolas Batum admitting they were “one or two plays away from maybe getting swept.” After the Clippers lost Game 2, workers cleaning Staples Center mused about the possibility of the series not returning to Los Angeles. As the Clippers lost Game 5, also at home, Clippers executive Jerry West left his courtside seat early during an unsightly stretch of fourth-quarter turnovers. And the nerves were cranked up high during Game 7 on Sunday, when Doncic scored 29 first-half points and the Mavericks opened the second half on a 17-6 run.

Given many chances to fold, the Clippers finally didn’t. Unlike in the bubble, where they squandered double-digit leads to the Nuggets in three straight losses to end the series, the Clippers came together in the toughest moments. Ballmer, seated courtside, couldn’t contain his joy, his arms spasming uncontrollably as he celebrated the Clippers’ 126-111 victory, which sent them to a second-round date with the Utah Jazz.

“Last year was last year,” Clippers Coach Tyronn Lue said. “We talked about that before the season started. We’ve got to keep looking forward. We can’t keep looking behind at what happened in the bubble. That s--- is over.”

It is for now, thanks to an impressive Game 3 comeback, a Game 6 victory in which Kawhi Leonard turned in perhaps the best performance of his playoff career and a Game 7 win in which the hot-shooting Clippers had seven players reach double figures. Leonard led the way again with 28 points, 10 rebounds and nine assists, and he was aided by 22 points, 10 assists and six rebounds from Paul George and 23 points from Marcus Morris Sr., an unlikely hero whose seven three-pointers earned him a bear hug from Ballmer in the closing seconds.

“These games aren’t won with just one or two great players,” Leonard said. “You need all 16 or 17 players. ... I’m not thinking about last year. I’m thinking about what we’re doing today and what the next step is tomorrow. I’m glad that we showed character and poise.”

Los Angeles absorbed Doncic’s best shot early and outlasted Dallas, which struggled to get consistent supporting-cast contributions throughout the series. Doncic posted 46 points, a playoff career high, to go with 14 assists and seven rebounds, but his teammates combined to shoot 5 for 25 on three-pointers. The Clippers closed the third quarter on a 24-4 run to take full control, and the vast gap in quality between Leonard’s cast and Doncic’s cast sent Dallas into the offseason needing to dramatically upgrade around its franchise player.

“That’s a question you should ask the guys that make decisions, right? I’m just a player here,” Doncic said when asked about the possibility of upcoming personnel moves. “But we will give everything to play great. We gave everything. I’m very proud of this team. Obviously I hate losing.”

This upside-down series, which saw the road team win each of the first six games, turned into a clash of styles as it unfolded. The Clippers, hoping to create space for their stars and improve their defensive matchups with Doncic, went with small and versatile lineups. The Mavericks countered by relying heavily on twin tower groups that featured two 7-footers, Kristaps Porzingis and Boban Marjanovic.

In Game 7, perimeter potency carried the day against sheer size. Dallas won the rebounding battle 47-35, but the Clippers, who led the league in three-point percentage, shot 20 for 43 from deep. Lue got 11 points and three three-pointers from backup guard Luke Kennard, who earned limited playing time this season, and the Clippers’ bench outscored the Mavericks’ reserves, 27-6.

While Leonard lapsed into passive play at times in the series, he was dominant on both ends in Game 6 — finishing with 45 points, six rebounds and three assists — and he struck the right balance between scoring and moving the ball in the closeout victory. His aggressive on-ball defense was key to wearing down Doncic, who had three 40-point games in the series.

“It all started with the big dog,” guard Reggie Jackson said, crediting Leonard with finishing off the Mavericks. “He came in with the mentality that he was going to take this game today. He was going to come in and lead and wasn’t going to be shy about his play at all.”

There was much consternation around the Clippers in recent weeks about what a first-round defeat against a lesser opponent would mean for the organization, especially if it transpired with a lack of backbone. Leonard will be the top free agent on this summer’s market, and Ballmer abruptly parted ways with coach Doc Rivers after the bubble catastrophe.

Those worries will be put on hold, at least temporarily. The Clippers joined the Nuggets and Milwaukee Bucks as the only teams to return to the conference semifinals after reaching that stage in the bubble, leaving a long-suffering team and fan base to savor a series win that featured triumph and relief. West and Ballmer shared a congratulatory handshake as the final seconds ticked off, and a delighted Lue balked when asked to dissect the series against the top-seeded Jazz.

“I mean, can we enjoy this one first?” he asked.