Eto'o, who made it six goals in three games, grabbed a brace and set up the other two goals for Javier Zanetti and Dejan Stankovic in a one-side first half.
However, the Nerazzurri's performance significantly declined after the break despite the fact the Tottenham keeper Gomes had been sent off since the eighth minute.
A sensational hat-trick from highflying winger Gareth Bale ensured that the Londoners come out of San Siro with their heads up.
Inter lead Group A on seven points, Spurs come second on four as Twente and Werder Bremen are tied on two points after drawing 1-1.
In Group B, Lyon remained in charge with a 2-0 victory over Benfica to reach nine points, Schalke moved to second with an easy 3-1 win over minnows Hapoel Tel-Aviv.
A first-half goal from Luis Nani was enough to give Manchester United a 1-0 victory over Bursaspor in Group C.
In Group D, Lionel Messi carried on the habit of inspiring Barcelona by scoring all goals in a 2-0 victory over Copenhagen.
Barca took charge of the group with seven points, one ahead of Copenhagen. Rubin Kazan held Panathinaikos 0-0 in Greece.