Inter produce ten-man turnaround
Inter went into the game in third and increased their lead over Lazio, a place behind them in the Serie A table before the fixture, to six points to strengthen their UEFA Champions League claims.
Mauro Zarate had given the visitors the lead in the first half, but Sneijder and Eto'o got the goals as Lazio also had Stefano Mauri sent off. Zarate had the first opening five minutes into the game and forced Julio Cesar into a difficult save.
Zarate pressed ten minutes later and beat two defenders but before he could shoot he was tackled by Andrea Ranocchia. The Argentinian gave Lazio the lead from the penalty spot after 22 minutes as the home side were reduced to ten men.
Julio Cesar brought down Zarate and was shown the red card, Diego Milito making way for substitute goalkeeper Luca Castellazzi, who was unable to save Zarate's penalty kick.
Lazio's lead was preserved by Fernando Muslera, who saved Dejan Stankovic's 25-yard drive and also Sneijder's close range follow-up. Zarate almost made it two for the visitors when he rounded Ranocchia but shot narrowly over.
Five minutes before the break Sneijder levelled the scores with a curling free-kick from 25 yards which left Muslera well beaten.
Sneijder shot wide six minutes into the second half before Eto'o got what proved to be the winner two minutes later. A counter attack saw Javier Zanetti feed Eto'o and he shot from close range past Muslera.
Castellazzi kept Inter in front with a save from Zarate after Stephan Lichtsteiner had set up the chance. Lazio's Andre Dias shot narrowly wide of the goal after Christian Ledesma had created the opening, but the visitors were then reduced to ten men.
Mauri was shown his second yellow card after a kick from behind on Yuto Nagatomo. Maicon fed Eto'o but his shot was saved by Muslera and then Zarate's header found Libor Kozak but his effort hit the bar.
Hernanes also shot wide from Javier Garrido's pass as Lazio again pressed for an equaliser. Muslera saved Maicon's shot and then the Brazilian's corner found McDonald Mariga but he headed wide. Lazio had one last chance but Zarate's cross was headed wide of the target by Tommaso Rocchi.