The Cameroon striker scored a hat-trick and the influential Wesley Sneijder was also on target as the Champions League holders showed they are still a force to be reckoned with despite the departure of Jose Mourinho.
- Inter Milan 4-0 Werder Bremen: As it happened
The hard work was done in the first 34 minutes, by which time the hosts were three up, Eto'o rounding off the win by completing his treble late on.
Victory lifted Rafael Benitez's men level on four points with Tottenham at the top of Group A.
Bremen were without three of their most experienced players - Claudio Pizarro, Clemens Fritz and Torsten Frings - through injury and their absences were keenly felt.
They threatened first with Hugo Almeida's shot from long range after four minutes which was parried by Julio Cesar, but that was as good as it got for the visitors in the first half.
Philippe Coutinho headed wide and Sneijder saw an effort blocked by goalkeeper Tim Wiese before Eto'o made the breakthrough in the 21st minute.
The Cameroon striker got goalside of defender Per Mertesacker from Esteban Cambiasso's pass and advanced into the area before squeezing a shot between Wiese's legs.
Eto'o struck again six minutes later, this time expertly bringing down a pass from Maicon before side-footing his right-footed finish inside the exposed Wiese's near post.
Bremen had no answer to Inter's attacking power and Wiese had to be alert to tip over a shot from Dejan Stankovic before Sneijder made it three in the 34th minute, following more fine work from Eto'o.
The striker's fine through ball picked out Sneijder's angled run and the Dutchman lifted a cool finish over Wiese.
Inter were forced to make a change in goal at the break, Luca Castellazzi replacing the injured Julio Cesar.
And the new keeper was tested early as he parried an effort from Wesley.
His opposite number then denied Coutinho before Inter lost Lucio to what appeared to be a knee injury just after the hour mark.
But Sneijder and Eto'o combined to deadly effect again in the 81st minute.
The Holland international's slide-rule pass from the left wing picked out the run of his team-mate and, as Wiese rashly hared off his line to the edge of the area, Eto'o calmly took the ball round him and put it into the empty net.
Bremen came close to a consolation late on but Castellazzi did well to keep out Marko Arnautovic's shot.