Late Inter comeback rescues point v Catania
Ranieri looked set for the chop after Alejandro Gomez and Mariano Izco gave the Sicilians a 2-0 half-time lead at a restless San Siro and the visitors could easily have notched a third before Inter hit back.
Lazio secured a 2-1 derby win over bitter rivals AS Roma who had goalkeeper Marten Stekelenburg sent off after eight minutes and Napoli's 2-1 win at Parma came courtesy of a hugely controversial late goal from Ezequiel Lavezzi.
Hernanes put Lazio ahead from the penalty awarded as a result of Stekelenburg's foul on Miroslav Klose, only for Fabio Borini to level six minutes later.
However, a 62nd-minute goal from Stefano Mauri enabled Lazio to go third in the table and complete the double over their neighbours after winning by the same score earlier in the season.
Lazio, in the Champions League play-off spot, have 48 points from 26 games, two ahead of faltering Udinese who were held 0-0 at home by Atalanta.
AC Milan lead with 54 points and Juventus, who have a game in hand, are on 51.
Ranieri has only been in the Inter hot seat since September but the former Chelsea, Juventus and AS Roma coach has been the subject of increasing speculation following a miserable run of four defeats in Serie A and one in the Champions League.
Ranieri dropped playmaker Wesley Sneijder from the starting line-up but the move back-fired when Gomez broke the offside trap to score with an angled shot in the 20th minute.
Eighteen minutes later, Giovanni Marchese broke down the left and cut the ball in for Gomez's fellow Argentine Izco to tap in.
Inter left the pitch at half-time to predictable jeers from a half-empty San Siro and Sneijder came on for the re-start.
With Inter attacking desperately, they were vulnerable to counter-attacks, one of which saw Gonzalo Bergessio just lob the ball over the bar.
Uruguay forward Forlan, who has had a difficult first season since his move from Atletico Madrid, began the fightback when he chested the ball down on the touch-line, twisted pass two defenders and scored with a vicious, swerving shot.
Argentina's Milito blasted the equaliser with 10 minutes left and an end-to-end finale could have seen a winner for either side with Felipe Seymour missing a good chance for Catania and Giampaolo Pazzini denied at point-blank range by Juan Pablo Carrizo at the other end.
The Rome derby got off to a fiery start when Klose broke through and appeared to be tripped by Stekelenburg. After taking his time to decide, the referee awarded a penalty and dismissed the Dutch goalkeeper amid furious Roma protests.
Brazilian midfielder Hernanes gave replacement goalkeeper Bogdan Lobont no chance from the penalty and celebrated with an ambitious somersault.
But Roma levelled when defender Juan's shot hit the post and Borini tapped in the rebound before Giuseppe Biava could clear.
After that, there were chances at both ends in a match also marred by constant histrionics and angry protests over almost every refereeing decision.
Mauri's winner was followed by copious amounts of time-wasting by Lazio, who had Lionel Scaloni dismissed in the 86th minute for a second yellow card and had a lucky escape from Francesco Totti headed narrowly wide.
Lavezzi scored an 86th-minute winner at Parma with the hosts claiming he was offside.
Cavani had given Napoli the lead before half-time, scoring from a rebound after his own penalty was saved by Antonio Mirante for his 16th league goal of the season. Cristian Zaccardo levelled for Parma in the 72nd minute.
Fiorentina beat bottom club Cesena 2-0, Lecce drew 2-2 at home to Genoa and Siena beat Cagliari 3-0.