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 played well in last week's 1-0 win at Sampdoria 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.
Sandro Tonali gave Milan a 12th minute lead with a stunning free-kick which was also his first Milan goal.
Alessandro Deiola's surprise header levelled the scores three minutes later but Milan only needed seconds to retake the lead through Rafael Leao.
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 the second goal in as many games from Jordan Veretout gave the capital club a deserved win.