Hernanes' goal for Lazio 30 minutes into a scrappy match lifted Vladimir Petkovic's team to 36 points, eight behind champions and league leaders Juventus, who won 3-1 at Cagliari on Friday.
"We worked hard for this, in the last month we have started to believe that we can do something important," Petkovic told Sky Italia before adding that they still needed to improve to challenge Juve for the title.
"We are doing better and better, we are more and more convincing, and some players are coming into form. We are doing well, but not well enough to compete with Juve," he said.
Andrea Stramaccioni's Inter dropped to fourth after Esteban Cambiasso's equaliser five minutes from time cancelled out Ciro Immobile's superb individual goal for second-bottom Genoa.
The 1-1 draw left Inter nine points off the top going into the Italian mid-season break.
"Today the result wasn't positive but I have to compliment the team, we're in a strange period," Stramaccioni said.
"The break is coming at a good time, now we're going to take our minds off things and come back stronger... things are right for a good 2013."
ROMA GO THIRD
Roma remained firmly in the race for a Champions League qualifying spot after beating Milan in an end-to-end thriller, with the visiting defence looking ragged.
Goals from Nicolas Burdisso, Pablo Osvaldo and two from the sensational Erik Lamela put the home side 4-0 up in just over an hour and the win moved Zdenek Zeman's flamboyant side into sixth place and within four points of Lazio.
"I'm happy with our display, especially the first half," said Roma manager Zdenek Zemanin, "the second half we tried to sit back on our lead but we don't know how to do that."
"It was a good game in the first half because we pressured them high up the field and were able to hit them on the counter-attack. In the second half we got pinned back though."
Roma had Marquinhos sent off with 13 minutes left for handball as Milan's Serie A top scorer Stephan El Shaarawy looked to be heading for a one-on-one with Mauro Goicoechea.
Milan staged a late rally with two goals in the last five minutes but it was too late to make up for their earlier defensive failings and the defeat left the club loitering in seventh, seven points off a Europa League qualifying spot.
"I think we need to improve our defending, but I did not see any big mistakes tonight," said defiant Milan coach Massimiliano Allegri. "Maybe we weren't aggressive enough on their counter-attacks, probably because we feared Roma's forwards."
"Sometimes games go against you and we contributed to the result, but at the end of the day I think Milan played well. Roma deserve credit for making the most of the space we left them."
JOVETIC DOUBLE
Fiorentina moved into third spot with a 3-0 win over troubled Palermo as Stevan Jovetic netted
