Atalanta set up an Italian Cup semi-final with Fiorentina after winning 2-1 at AC Milan on Wednesday, while Lazio won 1-0 in a fiery derby with Roma which finished with three red cards.

Teun Koopmeiners struck either side of half-time of an entertaining quarter-final to continue Atalanta's bid for a first major trophy since 1963, when they last won the competition.

"We have have done so much in recent years," said Atalanta coach Gian Piero Gasperini.

"We might not have any silverware... but we have reached the Italian Cup final in the past and we want to go all the way."

Rafael Leao put Milan ahead in the 45th minute following brilliant interplay with Theo Hernandez which ended with the Portugal winger stroking home a first-time finish.

Shortly before Gasperini had been sent off for his livid reaction to his team not being given a penalty when Milan's Tijjani Reijnders shoved Marten de Roon just as he looked set to prod home Charles De Ketelaere's knockdown.

De Roon instead clashed heads with Matteo Gabbia with such force that the pair were both forced to leave the field.

"The footage speaks for itself," added Gasperini.

"Nobody understands if it is VAR or the referee who is officiating, and that is a big problem.

"There is such a big difference in how certain incidents are dealt with. There's no clarity at all."

Instead of simply bemoaning their poor fortune Atalanta reacted immediately to Leao's opener when Koopmeiners swept home a superb shot on the stroke of half-time.

And just before the hour mark Netherlands midfielder Koopmeiners struck what turned out to be the decisive goal from the penalty spot, after Alex Jimenez brought down Aleksei Miranchuk.

This time it was Milan's turn to feel aggrieved as Jimenez appeared to clip the ball before touching Miranchuk, but again there was no VAR intervention on referee Marco Di Bello's decision.

"It wasn't a penalty, our player touched the ball, their player threw himself to the ground before being touched," said Milan boss Stefano Pioli.

"It's a shame because the cup was an objective for us, one that we don't have anymore. It's a bad night for us."

Mattia Zaccagni's penalty five minutes after the break in Rome set up a last-four clash with either Juventus or Frosinone, who play on Thursday.

"We're proud of the result because we think that our performance deserved it," said Lazio owner Claudio Lotito to Mediaset.

"Today the team showed itself to be a united and determined group, that's what a football team needs to be."

Zaccagni's spot-kick decided a match which featured plenty of tension but little in the way of goalmouth action.

Rival fans launched flares at each other before and during the match while Roma midfielder Edoardo Bove was hit on the neck by a beer bottle after being substituted for Stephan El Shaarawy in the 76th minute.

On the pitch Matias Vecino forced a save from Rui Patricio shortly before Zaccagni's decisive spot-kick, which was given for a foul by Dean Huijsen on Valentin Castellanos.

And Vecino twice went close afterwards as Roma struggled to create chances despite having star attackers Paulo Dybala and Romelu Lukaku on the pitch.

Dybala had to leave the field at half-time and his replacement Lorenzo Pellegrini couldn't add any attacking inspiration for the hosts.

The best Jose Mourinho's men could muster was Andrea Belotti's 86th-minute half-volley which was well saved by Christos Mandas, who then did brilliantly to stop Lorenzo Pellegrini poking in on the rebound.

Lazio forward Pedro and his Roma counterpart Sardar Azmoun were both sent off in stoppage time as tempers flared, while Roma defender Gianluca Mancini was also dismissed for dissent after the final whistle.