HOUSTON — Maybe it was fitting that James Harden’s shot kicked off the rim, took a bounce and received an unintentional assist from Jermaine O’Neal that carried the Rockets into the playoffs.

It was Harden himself who practically fell out of the sky right into the laps of the Rockets just four days before the start of the season that began the return to respectability and relevance.

“I didn’t know who was on the team. I didn’t know what was going on,” Harden said. “I was still kind of shocked. Weeks went by and a month went by. We kind of gained confidence in one another that we can go out and compete with anybody in this league. It’s been that way through this whole entire season and now we’re in the playoffs.”

The Rockets are back in the postseason for the first time in four years, having spent the past three springs with their noses pressed up against the window pane, tantalizingly close and yet locked out of the fun. For three straight years — with win totals of 42, 43 and 34 (in lockout-shortened 2012) — they had been the last team to miss out on the playoffs. Or took the best record into the draft lottery. Any way that you said it, the result was simply frustrating.

While team owner Leslie Alexander has been steadfast to “dive” for a chance at the bonanza offered by the draft lottery, general manager Daryl Morey has been more frantic than a one-armed juggler of chain saws to make and remake the roster again and again and again. It was that constant turmoil that led to exasperation by former coach Rick Adelman and an eventual parting of the ways. It has been an ongoing process that still puts constant new challenges into the path of coach Kevin McHale in his second season.

Even now, the Rockets are a laboratory project still in development. Houston is the NBA’s youngest team with an average age of 24.9 years and opened the season as the most inexperienced NBA team in the shot-clock era, based on minutes played.

The Rockets are the sixth-youngest team in history to reach the playoffs. The Thunder teams of 2010 and 2011, led by Kevin Durant and Russell Westbrook, are the youngest ever. Next in line are the Trail Blazers of 2009, led by Brandon Roy and LaMarcus Aldridge, the Bulls of 2006 with Luol Deng and Ben Gordon and the Hawks of 2008, led by Joe Johnson and Al Horford.

Despite Harden’s rapid rise to the league’s elite level, his first appearance in the All-Star Game and rank among the league’s top five scorers along with the likes of Carmelo Anthony, Durant, Kobe Bryant and LeBron James, the Rockets are still greener than most young sprouts of spring. Harden has been to the playoffs the past three seasons and went to The Finals last year with OKC, but is still only 23. Point guard Jeremy Lin is 24. Center Omer Asik is 26, but his is only his third year in the league and the first that he’s played starter’s minutes.

Though a 13-6 record over the past six weeks has made the return to the playoffs seem inevitable, it was not made official until Utah lost to the Thunder shortly after the Rockets beat Phoenix on Tuesday night.

“I actually didn’t think I would be excited,” Lin said. “I was like, ‘Oh yeah, we’re going for the six seed.’ Now that it’s really here, I’m actually really excited because no one really gave us a chance going into the season that we’d be in the playoffs.”

The Rockets have been a franchise stuck in a rut, mired in mediocrity since the glory days of their back-to-back championships in 1994 and 1995. While this is now their 18th winning record since the 1992-93 season — only the Spurs and Lakers have more at 19 — they have had precious little playoff success. In fact, the Rockets have won only a single playoff series — vs. Portland in 2009 — since 1997 when some of the names on the backs of the jerseys read: Olajuwon, Drexler and Barkley.

There was always hope and unfulfilled promise during the eras of Steve Francis, then Yao Ming and Tracy McGrady. But never the kind of results that were expected.

So when the wheeler-dealer Morey was able to land Harden on the eve of this season, it was the first step in his long held plan to put a franchise-type player on the court to build around and then supplement with the likes of Lin, Asik and Chandler Parsons.

In the process, the Rockets have turned into a fast-paced, 3-point shooting, prolific offensive club that most often produces the most entertaining games of any given night on NBA LeaguePass.

This will all lead into a summer of trying to land another big-name free agent, another All-Star caliber player, who can vault the Rockets back onto the level of title contenders.

But first things first and that was Harden’s shot that bounced high off the rim, O’Neal’s unofficial assist by goaltending and finally the Rockets taking an initial step back into the playoff conversation.