Goals either side of half-time from Luka Jovic and Christian Pulisic, and Fikayo Tomori’s close-range finish in the 74th minute gave injury-hit Milan the three points to relieve some pressure after being beaten by Borussia Dortmund midweek.Milan are unlikely to reach the last 16 of Europe’s top competition following Tuesday’s loss but are in decent shape at home despite wobbly form and nine first-team absences, including key attackers Olivier Giroud and Rafael Leao.

They are third, trailing Juve and three points behind second-placed Inter Milan, who will reclaim the summit in Italy’s top flight as long as they don’t lose at Napoli in Sunday’s big match.

Under-fire coach Stefano Pioli will be boosted by Jovic scoring his first goal for Milan since arriving in the summer, the Serb putting the hosts ahead in the 43rd minute just after Marvin Cuni wasted a glorious chance to give Frosinone the lead.

Pulisic doubled Milan’s lead four minutes after the break with a sumptuous piece of play, brilliantly controlling goalkeeper Mike Maignan’s boot upfield before carefully dinking home his fifth goal of the season.

And Tomori ended the match as a contest when he poked home Jovic’s knockdown, making Marco Brescianini’s late free-kick no more than a consolation goal.

Frosinone dropped down to 11th following their sixth defeat of the campaign, two points and places behind Lazio whose 1-0 win over 10-man Cagliari was greeted by loud disapproval from frustrated supporters.

Lazio are ninth after veteran Pedro’s eighth-minute winner but the manner of their slender victory enraged the home crowd who unleashed a volley of boos and whistles at the end of the match.

Cagliari were a man down from the 27th minute when Antoine Makoumbou was sent off for pulling back Matteo Guendouzi as the Lazio man raced through on goal.

But the away side went close to equalising twice in stoppage time as Ivan Provedel pulled off a magnificent save to deny Leonardo Pavoletti’s powerful header.

And just before the final whistle Manuel Lazzari nearly handed Gaetano Oristanio the leveller, leading to a barrage of boos for a team who on Tuesday reached the knockout stages of the Champions League for just the third time in the club’s history by beating Celtic.

“We won a difficult match, we’re more pleased with the result than we are with the performance, but the game with Celtic took a lot out of us,” said Lazio assistant manager Giovanni Martusciello.

Defeat left Cagliari just inside the relegation zone after Empoli earned a 1-1 draw at Genoa in the day’s early match and moved out of the bottom three.