The Roma game was scheduled for Saturday but the snow which has crippled Italy forced a one-day postponement.
Roma showed how impatient they were with a commanding victory which moved Luis Enrique's side to within two points of fifth-placed Inter.
Juan gave the hosts a 13th-minute lead and Italy Under-21 striker Borini, forging a name for himself in Serie A having gone under the radar while playing in England, scored his brace either side of the break.
Ranieri's return to Roma, from whom he resigned last term, became even more humiliating when Bojan Krkic made it 4-0 late on.
Flying Juve were surprisingly held to a home 0-0 draw with lowly Siena while uninspired champions Milan could not get past Napoli at a freezing San Siro where Zlatan Ibrahimovic was sent off on 64 minutes for slapping Salvatore Aronica.
Milan coach Massimiliano Allegri was sent to the stands for complaining.
Juve and Milan, separated by a point at the top, will at least have been pleased that third-placed Udinese went down 3-2 at Fiorentina and Lazio, who are fourth, lost 3-2 at Genoa in another cracking game where Bosko Jankovic netted twice for the hosts.
"Lazio are a really great side but we deserved our win," Genoa coach Pasquale Marino told reporters after his side stayed ninth.
Parma won 2-1 at Chievo, Palermo beat Atalanta 2-1, Lecce and Bologna drew 0-0 and bottom side Novara played out another goalless stalemate at home to Cagliari.
All the matches were played in the afternoon to avoid dipping temperatures in the evening. Cesena against Catania on Saturday was postponed to a date to be fixed.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.