Brazilian Gabriel Pec, Serbian Dejan Joveljic and Ghanaian Joseph Paintsil scored a brace each as the Galaxy turned on the style to set up a clash with the Seattle Sounders for a place in MLS Cup.
The Sounders eliminated the Galaxy's cross-city rivals Los Angeles FC on Saturday, but they will need to up their performance level a notch to get past a Galaxy team that is simply on fire.
The home side took less than a minute to get on the scoresheet when Spanish midfielder Riqui Puig, who was outstanding throughout the game, found Pec with a superb, defence-splitting pass with the outside of his foot.
Pec kept his composure as he cut inside past Jefferson Diaz and then beat Dayne St. Clair with a clinical finish.
But Minnesota responded just five minutes later in spectacular fashion with a thunderbolt from the edge of the box by Kelvin Yeboah.
The Galaxy continued to attack with intent and restored their advantage in the 18th minute when former Borussia Dortmund and Germany winger Marco Reus clipped in a cross which Joveljic met with a pin-point glancing header.
Paintsil made it 3-1 in the 37th, turning in a low cross at the back post, but again, Minnesota were quick to reply with Yeboah firing home a re-taken penalty.
Coming out for the second half 3-2 up, the Galaxy showed no interest in simply defending their lead and Pec produced a superb solo goal just five minutes after the restart.
Picking up the ball in his own half, the Brazilian powered down the right, leaving defenders in his trail before bursting into the box and firing into the far corner.
Pec had a chance for a hat trick when he was pushed over in the box by Diaz but saw his spot-kick superbly saved by St. Clair.
Diaz was given his marching orders after picking up a second yellow for another arm in the face of Pec before goals from Paintsil and Joveljic completed the rout.
Orlando City advance
Argentine Ramiro Enrique did what Lionel Messi couldn't do and eliminated Atlanta United from the MLS playoffs as Orlando City reached the Eastern Conference final for the first time with a 1-0 win.
Enrique struck in the 39th minute and Orlando held firm in the second half as Atlanta's dream of a run to MLS Cup, after their shock win in the first round against Inter Miami, ended in Central Florida.
Orlando will host the conference final next weekend against New York Red Bulls, who defeated New York City on Saturday.
Orlando were on the front foot from the outset -- in the 5th minute, Facundo Torres broke down the left and slipped the ball across to Dagur Thorhallsson, but the Icelandic winger's shot struck the post.
Chances were at a premium until Orlando broke through, six minutes before the interval, when Atlanta failed to clear a corner and Enrique pounced, sliding in and scooping a shot past Brad Guzan.
Atlanta suffered another blow moments later when striker Jamal Thiare went down injured and had to be replaced by Daniel Rios.
It got worse for the visitors when, four minutes after the interval, substitute Rios was hit by the ball and had to be replaced due to concussion.
Orlando were solid at the back and had chances to put the game to bed but were unable to capitalise.
"I thought we had a lot of energy, especially in the first half," said Orlando coach Oscar Pareja.
"It is one more step closer to our objective but now we can prepare for the next one," he told Apple TV.
The game marked the final appearance of Atlanta's Dax McCarty, the former USA international midfielder who is retiring from game at the age of 37.
McCarty, who grew up near Orlando, said the "magic ran out" for Atlanta.
"It has been one of the most memorable months of my career, frustrating season but we ended it with pride and ended it fighting and that's all you can ask," he said.
