Roberto Mancini's Inter extended their streak without a victory to four matches and spurned the opportunity to usurp Fiorentina as leaders after Alberto Gilardino cancelled out Ivan Perisic's opener.
The draw left Inter second on 18 points, the same as Fiorentina who have a game in hand. Palermo are 11th on 11.
The visitors struck after 60 minutes when a magnificent chip from Stevan Jovetic found Jonathan Biabiany advancing into the box. The substitute brought the ball down before crossing to Perisic who finished calmly at the far post.
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Gilardino equalised six minutes later after reacting quickest in a goalmouth melee to tap the ball past Samir Handanovic from close range.
Mancini made four changes following the 0-0 draw with Juventus last weekend and his side lacked cohesion early on.
Handanovic made two saves from Franco Vazquez while the Palermo forward also sent a header just over the bar after outmuscling Joao Miranda.
Inter's Jeison Murillo was shown a second yellow card in the 79th minute for bringing down Vazquez with a poorly-timed challenge.
Struggling Carpi took the lead against local rivals Bologna when Gaetano Letizia struck after 24 minutes but they were reduced to 10 men before the break when Lorenzo Lollo was dismissed.
Captain Daniele Gastaldello equalised for Bologna in the 47th minute. Adam Masina then tapped home the winner in stoppage time following indecision from goalkeeper Vid Belec. Bologna leapfrogged their opponents into 18th place with six points while Carpi dropped to the bottom on five.
"I am sorry for the boys because they put in an extraordinary performance," Carpi coach Giuseppe Sannino told Sky Sport Italia. "Before the red card we were the only team playing and then the attitude changed.
"I am disappointed the people of Carpi booed instead of applauding these lads for their efforts. We have a very arduous task to keep this side in Serie A."
Goals from Rade Krunic and Piotr Zielinski gave Empoli a 2-0 victory over mid-table rivals Genoa.
Among the seven games to be played on Sunday, Fiorentina host third-placed AS Roma and Atalanta travel to Juventus.
(Writing by Ed Dove; Editing by Tony Jimenez)
