Gonzalo Higuain hit a hat-trick to set a new all-time record of 36 goals in a single Serie A season as Napoli secured second spot and Champions League football with a dramatic 4-0 rout of 10-man Frosinone.

Roma, despite a 3-1 win at AC Milan that has virtually ended the hosts' hopes of Europa League football, finished two points further adrift in third meaning they will enter the preliminary rounds of Europe's premier club competition.

Champions Juventus, who secured a record-equalling fifth successive title last month, capped their campaign on Saturday with a 5-0 rout of 10-man Sampdoria in Turin where Paulo Dybala struck twice for the hosts.

It left the remaining European places for next season as all that was left to be decided, and Napoli and Sassuolo emerged the victors.

Roma, runners-up the past two seasons, travelled to Milan looking for a win and hoping Napoli would stumble at home.

But despite goals from Mohamed Salah, Stephan El Shaarawy and a late Emerson strike, with Carlos Bacca hitting a late consolation for the Rossoneri, it was not enough for Luciano Spalletti's men.

In scenes not seen since the heady days of Diego Maradona on their second title win in 1990, Napoli fans had packed out the San Paolo stadium hoping to see local hero 'Pipita' set a new record.

Sitting on 33 goals, Higuain was still two short of Gunnar Nordahl's 1950 record of 35, scored in a 20-team, Serie A campaign.

Frosinone gave Napoli, and Higuain, plenty of incentive after Mirko Gori was shown a straight red card for dissent, moments after a challenge on Napoli winger Lorenzo Insigne.

Higuain had the ball in the net just after the half hour, but the Argentine was offside and it took until the 44th minute for the hosts to capitalise, captain Marek Hamsik powering home from Faouzi Ghoulam's cross.

Higuain flashed a shot over the bar minutes after the restart, but made amends in the 52nd minute with his 34th goal of the campaign after sending Allan's low cross past Massimo Zappino.

A packed San Paolo erupted, but more was to come from the former Real Madrid striker.

Higuain had his second of the night, and record-equalling 35th when he glanced Jose Callejon's cross past Zappino just after the hour.

When Higuain hit his third of the night ten minutes later, it was a wonder strike from outside the area that he took on the turn and left Zappino with no chance.

Higuain could have finished with more goals. He served a three-match ban last month as punishment for pushing the referee in a 3-1 defeat at Udinese.

Elsewhere, Sassuolo boosted their hopes of Europa League football next season with a 3-1 home win over 10-man Inter Milan which left them in sixth place and one point ahead of Milan.

Milan can secure Europa League football if they upset predictions and beat Juventus in the Italian Cup final on May 21.

The Cup winner is awarded the competition's final spot. If they don't, the seven-time European champions will see Sassuolo, as sixth place finishers, go into Europe.