The Rossoneri fought back from a goal down to take a commanding lead in the tie and are firm favourites to finish the job at the San Siro.
Roma captain Francesco Totti gave the hosts the lead on 28 minutes, but a brilliant second half showing turned the game in Milan's favour.
Three goals in a devastating ten-minute spell put the visitors in total control.
Brazilian ace Serginho drew the sides level converting from the penalty spot on 62 minutes after Christian Panucci handled the ball in the area.
Massimo Ambrosini fired Milan in front after 70 minutes when his header deflected off Jonathan Zebina and into the net.
Serginho added a third with his second of the night just two minutes later - breaking the offside trap to slot past Ivan Pelizzoli.
Substitute Andrei Shevchenko then completed the rout with the fourth goal a minute from time with a superb lob.
The result all but renders the second leg on May 31 a mere formality - unless Roma can produce a memorable comeback.
