France forward Giroud, who has not been picked for Les Bleus’ upcoming World Cup qualifiers, bagged a brace in a 4-1 win over Cagliari at the San Siro while Abraham scored in a 4-0 rout at promoted Salernitana.
Both strikers left European champions Chelsea this summer in the search of more regular football and have got off to quick starts in Italy.
Giroud has been given the number nine jersey at Milan and scored the third and fourth in an easy victory at the San Siro.
His name was sung by a large portion of the 31,000 Milan fans present, who watched their team run riot in a highly entertaining first half which won the match for Stefano Pioli’s team.
“I am very proud to play for Milan and to play in the San Siro stadium. It is a great emotion,” Giroud said.
“I believe in myself and in my abilities. As a child I used to watch Van Basten, Papin and Inzaghi and wearing this shirt makes me happy.”
Sandro Tonali gave Milan a 12th minute lead with a stunning free-kick which was also his first Milan goal, and Rafael Leao claimed the second after Alessandro Deiola’s surprise header levelled the scores.
Giroud then artfully guided home his first Milan goal following a superb run and pass from Brahim Diaz, and when Kevin Strootman’s handball was judged to have taken place in the penalty area by VAR, the 34-year-old stepped up and stroked the spot-kick home.
Abraham meanwhile crashed home the third in the 69th minute at Salernitana as a flurry of second half goals gave Jose Mourinho’s team a comprehensive win in the Italian south.
Roma struggled to break down the hosts in the opening period but a double from Lorenzo Pellegrini and a third goal in two games from Jordan Veretout gave the capital club a deserved win.
“I was perfectly calm right from the start. The team played really well… Again tonight, we dominated the match,” said Mourinho.
Both teams sit in a pack of five on a perfect six points, which also includes leaders Lazio, Inter Milan and Napoli, who earlier got a hard-fought 2-1 win at Genoa thanks to Andrea Petagna’s late header.
Italy international forward Petagna, who was named a substitute despite the absences of both Victor Osimhen and Dries Mertens, was reportedly set to join Sampdoria on loan this transfer window.
However with the match level through goals from Fabian Ruiz and Genoa academy graduate Andrea Cambiaso he entered the field with eight minutes remaining at the Marassi stadium and two minutes later was wheeling away in celebration after his bullet header gave Napoli the decisive goal.
“I didn’t expect to be still here, there’s been a lot going on this week, but I wanted to show what I think I’m worth,” the imposing forward told DAZN.
“It was great coming on and scoring, but honestly with my shape it’s hard work, I need to play more regularly to feel right on the pitch.”
Sassuolo and Sampdoria played out a goalless draw in the other early match, with Emil Audero putting in a great performance in the Samp goal to escape with a point.