LOS ANGELES -- It wasn't until three minutes remained in LAFC's 5-3 win over the LA Galaxy that the home fans in Banc of California Stadium indulged themselves by yelling "Ole!" with every completed pass. One couldn't blame them for waiting to the very end.

In the brief history of this rivalry, LAFC has blown leads in all manner of ways. There have been moments of individual brilliance from Galaxy forward Zlatan Ibrahimovic and backbreaking defensive breakdowns that had to be seen to be believed. LAFC's fans had been conditioned to expect the worst. Thursday's victory in the Western Conference semifinals was the payoff, with LAFC winning for the first time in six encounters. But even as the result was different, there were similarities too, some of the haunting variety.

The Black and Gold surged in front thanks to two Carlos Vela goals, but by the 51st minute the Galaxy was back even, with nemesis Ibrahimovic netting the equalizer through goalkeeper Tyler Miller's legs. Goals two minutes apart from Diego Rossi and Adama Diomande saw the home side surge back in front, only for the Galaxy to grab one back through Rolf Feltscher. With nerves jangling, Diomande finally made the game safe in the 80th minute, and when the final whistle blew, the home fans roared.

LAFC finally slew its dragon.

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"When you've had games that get away from you, there's got to be some lessons along the way," said LAFC manager Bob Bradley. "At some moment, against your biggest rival, when obviously everything is at stake, to see those guys respond at 2-2, man that was awesome. That's such a step for this group."

Those lessons were reflected in Bradley's tactical approach to start the game. In previous matches, the Galaxy had ridden the jolts of adrenalin provided by Ibrahimovic's individual brilliance. And in many cases, LAFC's desire to carry the game was used against it to make the game more wide open than it needed to be.

This time around, the home side was content to sit back and absorb some pressure rather than insist on carrying the game to the Galaxy. Not only did that prevent the visitors from creating transition opportunities, but it took away space underneath and prevented Ibrahimovic or Cristian Pavon from latching onto loose balls and then playmaking in central areas.

And when the opportunity was there for LAFC to counter, it did so in ruthless fashion with the attacking trident of Vela, Rossi and Brian Rodriguez -- aided by the ball-winning of Latif Blessing -- turning the Galaxy's backline into knots. Vela in particular dazzled with his ability in transition.

But that only took the Black and Gold so far. For LAFC, composure is a trait that has often evaporated against its crosstown rival. So it was left to the team's collective head to see it through and it showed in the team's will to finish plays in attack and it did just enough defensively to see the result out. Diomande, recently returned from a stint in the league's Substance and Behavioral Health program, provided a huge boost.

The question now is: does LAFC have anything left? There are two more dragons left to slay in order to achieve its Supporters Shield/MLS Cup double. Up next is a tricky encounter against the Seattle Sounders on Tuesday, a side that has the benefit of an extra day's rest. Bradley noted his team's defensive frailties on the evening, even if they were somewhat overshadowed by the magnitude of the victory.

"There's a proud feeling of how we keep moving ourselves along, and yet when you talk to everybody inside, they're all focused already on the next game," said Bradley. "You can tell that this was just an important win. But we've got to move on...These playoffs games and this format, man, they're crazy. So we have to rebound quickly."

That is easy to say, yet harder to execute. But at least LAFC is moving on, which is something that the Galaxy can only look at with envy. The Galaxy can't feel cheated either, though there will remain some clamoring that Rodriguez was offside in the buildup to Vela's second goal. On this night, a Galaxy defense that had been sieve-like all season reverted to type following its first-round win against Minnesota United. The decision of Galaxy manager Guillermo Barros Schelotto to deploy four center-backs in his backline smacked of desperation, and on this night, there was simply no dealing with the dynamic movement of LAFC's front three.

"The whole season has been, we score a couple of goals and we concede much more than we score," said Ibrahimovic. "We should be sad and disappointed. We made mistakes and they punished us."

Ibrahimovic did have a goal and an assist on the night, yet his contribution was more of a spark rather than the raging inferno of previous encounters with LAFC. At the final whistle, he didn't shake any hands, opting to go straight to the locker room. Afterward he complained he had difficulty breathing due to a sore throat, and that he didn't know if it was due to the wildfires in the Los Angeles area.

Inevitably, questions turned to whether the Swede has played his last game in MLS. He has certainly lifted the league up and provided a priceless amount of attention. He responded with a series of maybes, adding it was "too early to speak" before ending with a typical Zlatan response.

"[If I stay], then MLS is good, because the whole world will watch it," he said. "If I don't stay, nobody will remember what MLS is."

The truth is that LAFC's attack, and Vela in particular, are delivering plenty of memories. The challenge to be remembered as champions goes on.