Lionel Messi started the first of two counterattacks for Neymar to strike right back in the ninth minute. (Source: Reuters)

Neymar scored twice to lead Barcelona past nine-man Atletico Madrid and into the Copa del Rey semifinals with a 3-2 victory in a game that went from pulsating to unseemly at Vicente Calderon Stadium on Wednesday.

Barcelona advanced 4-2 on aggregate to set up a meeting with Villarreal or Getafe after an incident-filled match that saw three beautiful goals, questionable refereeing decisions, an own goal and a sending off at halftime. Not to mention Atletico’s Arda Turan losing his temper and tossing his shoe at a linesman.

Barcelona entered with a 1-0 cushion from the opening leg, but Atletico’s Fernando Torres needed just 39 seconds to score and set off an electric first half.

Lionel Messi started the first of two counterattacks for Neymar to strike right back in the ninth minute.

The match swayed again when Atletico’s Raul Garcia converted a penalty on the half-hour mark, but Miranda’s own goal put Barcelona back in control before Neymar pounced again on another Messi-led break before halftime.

Atletico’s self-destruction continued when Gabi Fernandez earned a second yellow at halftime for arguing with the referee following a scuffle between the teams. Turan was fortunate three minutes after the restart to only receive a yellow for throwing his shoe at the linesman. Mario Suarez then was ejected in the 84th for his second booking.

All that produced a rare sight in the second half: a Diego Simeone-coached Atletico without any fight left in them, down three goals and eventually two men.

“I am proud of my players, they were extraordinary in the first half,” Simeone said. “In the second half the team played as I asked them to, trying to not let them score and without any aspirations to score either. I thought it was the most opportune decision for my team.”

After failing to beat Atletico in six meeting last year, when the Madrid team won the Spanish league and reached the Champions League final, first-year coach Luis Enrique has led Barcelona to three wins over Simeone’s side.

It was Barcelona’s seventh consecutive win since a loss at Real Sociedad had put Luis Enrique under intense pressure to turn things around.

“The season is long with many ups and downs, we are in a good moment, with a lot of confidence and playing well,” the coach said.

Torres stunned Barcelona with his early goal when he skillfully controlled a long ball, used one touch to open an angle around Javier Mascherano before firing a long strike in off the post.

But Barcelona responded with a blistering counterattack when Messi dribbled by Mario Suarez and passed for Luis Suarez, who in turn played Neymar free to beat goalkeeper Jan Oblak with an angled shot.

Juanfran Torres drew a foul by Mascherano that the referee judged inside the area but televised replays showed to be outside, allowing Garcia to score from the spot.

But the home crowd fell silent when Miranda directed Sergio Busquet’s off-target header into his own net in the 38th.

Atletico clamored for another penalty when Antoine Griezmann volleyed Siqueira’s cross into Alba’s arm. The referee was unmoved and seconds later Messi was crossing for Alba to knock the ball down for Neymar to coolly put past Oblak.

After the glut of goals in the first half, the game suddenly descended into a series of ugly incidents.

Messi was booked for booting a ball into the stands. Then Torres and Neymar exchanged heated words as the teams left the pitch at halftime, an argument that sparked a shoving bout between several members of both benches.

Gabi sunk the hosts’ chances with his sending off, and Turan almost followed his captain when his temper boiled over after a tackle left him without a shoe. With no foul call forthcoming, the Turkey midfielder angrily tossed his shoe over the head of the linesman.

Villarreal visits Getafe with a 1-0 lead on Thursday, while Espanyol visits Sevilla up 3-1. Athletic Bilbao also hosts Malaga after their scoreless draw.