Sneijder curled an inch-perfect 73rd-minute free-kick into the right-hand side of the goal and rattled the outside of the post with another before Eto'o sealed the win in the last minute, dribbling into the area from the left and then beating Gianluca Curci, the Sampdoria goalkeeper.
The result leaves Inter just two points behind table-topping city rivals AC Milan, though they have played a game more.
Delio Rossi, the Palermo coach, insisted he will not resign despite his side suffering a humiliating 7-0 home defeat to Udinese.
Alexis Sanchez scored four of the goals and Antonio Di Natale also grabbed a hat-trick while Palermo, who trailed 5-0 at half-time, had Armin Bacinovic and Matteo Darmian sent off.
"I will not resign, it's not my style. I am combative and I just don't leave at the first sign of trouble," Rossi said.
Carvalho Amauri, the Parma striker, scored twice in the second half as Roma threw away another lead to draw 2-2 at the Stadio Olimpico.
Francesco Totti converted from the penalty spot in the 19th minute and teammate Juan made it 2-0 before half-time.
But Amauri reduced the deficit in the 74th minute before adding his second five minutes later.
Brescia also threw away a two-goal lead as they had to settle for a 2-2 draw with fellow strugglers Lecce.
Two goals in as many minutes from Andrea Caracciolo and Davide Zoboli had given the home side the edge, but Lecce hit back through Daniele Corvia and Gianni Munari.
Luis Jimenez's late penalty earned Cesena a priceless victory 1-0 win against Chievo in their fight against relegation from Serie A.
The home side dominated the game but could not find a way past visiting goalkeeper Stefano Sorrentino and looked as though they would have to settle for a point until Davide Madelli's foul on Erjon Bogdani a minute from time allowed Jimenez to seal all three points.
Substitute Abdelkader Ghezzal fired a late equaliser for rock-bottom Bari to deny Fiorentina a second away win of the season.
Alberto Gilardino's 21st-minute strike had looked to have put La Viola on course for three points at the Stadio San Nicola, but Ghezzal — a 73rd-minute replacement for Jaime Romero — earned a 1-1 draw three minutes from time.
Lazio's five-match unbeaten run came to an end as Andre Dias' own goal condemned them to defeat at Cagliari, while Catania came from behind to beat Genoa in a pulsating game at the Stadio Massimino.
Antonio Floro Flores put Genoa in front in the 19th minute, but goals from Maxi Lopez and Gonzalo Bergessio early in the second half turned the game on its head.
Referee Antonio Giannoccaro then showed red cards to Domenico Criscito and Blazej Augustyn, failed to give one clear penalty and awarded another controversial one, which was missed by Genoa midfielder Miguel Veloso.