The Belgian striker fired in his 18th league goal of the season to register his club’s second-fastest Serie A strike since Opta started taking records in 2004.
Lukaku also set up former Manchester United teammate Matteo Darmian for Inter’s second after 69 minutes and was again involved in the third goal, when his shot was saved but headed in on the rebound by substitute Alexis Sanchez.
Inter also had many chances to add to their tally during the game as Nicolo Barella’s curling strike hit the bar while Lukaku had a powerful effort saved by Mattia Perin.
The visitors can also give plaudits to their goalie, Perin, who kept the score down as he denied Danilo D’Ambrosio and Sanchez with superb diving saves late on.
Watch the highlights of the match below
Roma 1-2 AC Milan: Milan secured a difficult away victory to keep the pressure on Inter
AC Milan returned to winning ways with an enthralling 2-1 victory away to a difficult AS Roma side and also restored a four-point gap to Serie A leaders Inter.
The visitors hit the crossbar and had two goals disallowed before Franck Kessie scored from the penalty spot to give them a deserved half-time lead.
Roma, who also had a goal ruled out in the first half, responded as quickly as possible after the break when midfielder Jordan Veretout curled in his 10th league goal of the season.
However, a superb turn and finish from Ante Rebic put the visitors back in front after 58 minutes and they held on despite late pressure from the hosts.
The victory ends a four-match winless run in all competitions for Stefano Pioli’s side, whose hopes of a first Serie A title in 10 years suffered a blow following back-to-back league defeats to Spezia and Inter.
Milan are currently second on 52 points, four behind Inter, and six ahead of Juventus in third, while Roma stays fifth with 44 points.