The match in Sardinia was briefly held up after just three minutes as Eto'o suffered racist taunts from the home side's 'ultra' fans.
Following a stadium announcement reminding those fans that the game could be abandoned if they continued, the match resumed with Eto'o proving the hero.
He even brushed off the chants by mimicking a monkey after scoring.
Eto'o now has 12 goals in 11 games this season but coach Rafael Benitez insists his team is not over-reliant on the hitman ahead of Wednesday's Champions League clash against Tottenham.
"He's in great form and that's a good thing for us but we can score in a variety of different ways," said the Spaniard.
"Obviously the better you play, the easier it is to win but it's important to win to give us confidence.
"We made one or two mistakes and (Cagliari) could have been dangerous.
"Now we'll think about Tottenham. It will be tough, they have speed and ability. We'll have to play a great match."
However, Lazio can reclaim the summit if they win away to Bari in Sunday's late match.
Cagliari had the first clear chance when Belgium international Radja Nainggolan teed up Andrea Cossu, whose precise finish flashed wide.
Inter's Brazilian full-back Maicon tried his luck from distance but also missed the far post.
Philippe Coutinho then cut in from the left and played a one-two with Eto'o before shooting too close to goalkeeper Michael Agazzi.
When the Inter breakthrough came it was thanks to Eto'o's brilliance on 39 minutes.
Alessandro Agostini failed to clear his lines properly and the ball spun into the air off Wesley Sneijder.
Eto'o plucked the ball out of the air with a piece of sublime control using his right foot, then shifted onto his left, leaving Davide Astori bamboozled, and finished crisply inside the post.
To celebrate, the Cameroon forward mocked those who had abused him by imitating a monkey.
Cagliari had a double chance to hit back five minutes after the restart but Nene took an age to shoot and when he did Julio Cesar parried, jumping up to then push Alessandro Matri's follow-up around the post.
At the other end, Agazzi dived to his left to tip over a curling Eto'o effort.
Inter had a let-off 14 minutes from time when Robert Acquafresca's cross deflected off Cristian Chivu and came back off the bar, with Daniele Conti able only to prod the rebound into Julio Cesar's grateful arms.
Conti had another chance to snatch a share of the spoils but when teed up by Cossu, he volleyed high over the bar.
Juventus and Palermo both moved to three points from the summit after knocking in four goals each.
Alberto Aquilani, a Felipe Melo penalty, Fabio Quagliarella and Alessandro Del Piero scored in Juve's 4-0 defeat of Lecce sending them fifth.
Javier Pastore, Mauricio Pinilla and Slovenian pair Josip Ilicic and Armin Bacinovic netted for the Sicilians in their 4-1 success against Bologna to go sixth.
Fourth-placed Napoli missed the chance to join the Milan neighbours at the top as they drew 1-1 at Catania while Fiorentina went bottom following their 2-1 reverse at Sampdoria.
Alexandre Pato scored a brace and Robinho notched his first goal for Milan in their win on Saturday, while Roma earned only their second success of the season as Marco Borriello netted in their 2-1 win over his former club Genoa.
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