Vela double sends Ibrahimovic, Galaxy crashing out of playoffs
Mexico international striker Vela took his season goal tally to 36 with two first half strikes at the Banc of California Stadium.
Ibrahimovic led a rousing Galaxy fightback, setting up a Cristian Pavon goal before grabbing an opportunistic second-half equaliser to make it 2-2.
But LAFC hit back with goals from Diego Rossi and substitute Adama Diomande to surge into a 4-2 lead.
A headed goal from Galaxy substitute Rolf Feltscher raised hopes of another comeback, but Diomande's second of the night made the game safe.
It was a first ever win for LAFC over the Galaxy, a burgeoning Major League Soccer rivalry that has been dubbed "El Trafico" in a reference to the Californian city's notorious traffic.
LAFC will now face the Seattle Sounders in the Western Conference Championship final next Tuesday for a place in the MLS Cup final.
Galaxy had started the stronger of the two sides and came closest to opening the scoring early on when Pavon's shot deflected off Tristan Blackmon and struck the post.
But it was not long before LAFC's potent front three began to make their presence felt, Vela releasing Brian Rodriguez with a clever through ball only for the Uruguayan teenager to shoot over.
Vela then rattled the woodwork shortly afterwards, with a curling a free-kick from 25 yards.
On 16 minutes, the Galaxy's defence finally cracked.
Latif Blessing dispossessed Diego Polenta in midfield and Lee Ngyuen and Rossi combined to free Vela.
The MVP candidate cut inside and calmly placed his finish beyond David Bingham.
It got better five minutes from half-time with another superbly worked goal that doubled the home side's lead.
Rodriguez ghosted down the left and worked a 1-2 with Blessing before squaring for Vela for the simplest of finishes.
It could have been a hammer blow for Galaxy, but the visitors responded immediately, Ibrahimovic holding off his markers to free Pavon on the left.
The Argentina striker made no mistake, rifling low past Tyler Miller to make it 2-1.
The fightback was well and truly on when Ibrahimovic blasted a shot through Tyle Miller's legs on 55 minutes.
But Los Angeles hit back with two goals in two minutes, Rossi finding the net in the 66th minute before Diomande's header capped a sweeping counter-attack in the 68th minute.
Galaxy substitute Feltscher ensured a nervous finish after heading home Romain Alessandrini's free-kick in the 77th minute.
Diomande however grabbed his second of the night 10 minutes from time, turning Polenta in midfield and chipping over Bingham for 5-3.