The Rossoneri lie fifth in the table following the result, 21 points behind league leaders Juventus, and five points behind city rivals Inter in third. Both sides also have a game in hand over Gattuso’s men.
Failure to find the back of the net now means that Milan have not scored in their previous four league matches - a barren spell that surpasses any they have endured in the past 34 years.
Gattuso has not seen his side win a match since the beginning of December, with the Italian giants also suffering a 3-1 loss to Olympiacos in the Europa League.
The draw also means that Milan have failed to record a victory in any of their last eight fixtures against newly promoted clubs, drawing four and losing two. Their last win over a promoted side came in the 4-0 win over SPAL back in February.
Firing another blank in front of goal means that the Rossoneri have not scored a goal in the first half of a league match since their 2-1 win over Genoa at San Siro in October.
The club’s barren run coincides with a personal dry spell for Argentine striker Gonzalo Higuain. The 31-year-old has failed to register a strike in his past 802 minutes in all competitions, as he continues to endure a torrid loan spell from parent club Juve.
The forward was part of an insipid front line that had 25 efforts on goal without success against the team from Lazio - the most they have recorded in any Serie A match away from home this calendar year.
Milan’s next league outing comes on Saturday evening, when they host SPAL at San Siro. The side from Ferraro lie 16th in the table, just three points ahead of 18th placed Bologna.