Roma fans buzzed around the city honking their car and scooter horns after Ranieri's men moved one point ahead of champions Inter, who were held 2-2 at Fiorentina on Saturday, with five games to go.
NEWS:Roma overtake Inter at top
The leading pair both have difficult games next weekend. On Friday, Inter face a Juventus side striving to climb into the top four to qualify for the Champions League, while Roma meet city rivals Lazio on Sunday.
"They have a vital match for their bid to catch us up again. We have a tough cat to skin (against Lazio)," Ranieri told Sky television after his side extended their unbeaten league run to 23 games to return to the summit of Serie A after over two years.
"There are five games to go and we have to play with great humility. They will be five hard matches. We have to take them one at a time. Before others were in control, now it depends on us," he added.
AC Milan boss Leonardo was not throwing in the towel after his side, in third, slipped four points off the pace when they were held 2-2 at home by Catania.
"We are not giving up," said Leonardo after Milan rallied to claim a draw with a Marco Borriello double after being 2-0 down at half time.
"After our second-half performance I'm more optimistic. We gave away a half but then we dug out our character and pride and this makes me happy.
"Inter have had some slips. Roma are the most in-form team but they have hard games. We are there, still fighting, which shows other teams slip up like we do."
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