Weah struck within 11 seconds of the restart and again after 64 minutes to give Milan their first league victory in Turin over their rivals since March 1994.
Milan feel they now have a 16th league title within their grasp. Their two remaining fixtures are against relegated Empoli and faltering Perugia while Lazio face a tough trip to Fiorentina next weekend followed by a make-or-break home game against Uefa Cup finalists Parma on the last day of the season.
"We just have to close our eyes and forget about what's happening elsewhere in the championship now," said Zaccheroni, seeking to win the Scudetto in his first season at Milan. "Hopefully when we open them again in a fortnight's time we'll be champions."
In Rome, a nervous Lazio finally broke the deadlock against Bologna. The Argentinian midfielder Matias Almeyda picked up a ball on the edge of the box and fired an unstoppable shot past goalkeeper Francesco Antonioli for his first Serie A goal.
Christian Vieri finally settled the game in injury time, linking up with Roberto Mancini before firing home a left foot shot.
Lazio now have 65 points to Milan's 64 while Parma and Fiorentina have 55 and 54 respectively. Fiorentina squandered a 2-1 lead to lose 3-2 at relegation-threatened Sampdoria, ending the match with nine men. Sandro Cois was sent off in the 33rd minute and Pasquale Padalino followed in injury time.
Striker Vincenzo Montello scored twice for 1991 champions Sampdoria, who nevertheless remain anchored one place above the bottom. Parma won 3-1 at Internazionale on Saturday to overtake Fiorentina.
Manchester United's European Cup opponents Bayern Munich made sure of their 15th German title with a 1-1 draw at home to Hertha Berlin yesterday. They now have an unassailable 10-point lead over second-placed Bayer Leverkusen with three games remaining.
In Brussels, Genk, needing a win to clinch their first Belgian title, were handed a 5-2 drubbing by resurgent Anderlecht. However, with one match left, Genk maintained their two-point lead over Club Bruges after the champions went down 2-0 at Excelsior Mouscron.
In Paris, Lens won the first cup final in their 90-year history when they beat Metz 1-0 in the French League Cup final on Saturday. Midfielder Daniel Moreira blasted home the winner in the 56th minute to secure the reigning league champions a Uefa Cup spot next season.Reuse content