The Cameroon international struck in the 71st and 80th minutes after Goran Pandev had cancelled out John Arne Riise's opener for Roma in the first half.
The goals ensured Inter bagged their fourth title of the year after they won an unprecedented Champions League-Serie A-Italian Cup treble under Jose Mourinho last season.
The Super Cup is usually played between the Serie A and Italian Cup winners but with Inter claiming a clean sweep, Roma took part in this season's curtain-raiser because they were runners-up in both domestic competitions.
"I'm very happy. We showed character after we conceded the goal," coach Benitez told Rai television.
"Clearly, today was our first official match and it wasn't easy for us. It's hot and some of the players returned to the club late (after the World Cup).
"The most beautiful thing of the night was the team's reaction."
SAME LINEUP
Benitez fielded the same starting lineup Mourinho used to sink Bayern Munich 2-0 in May's Champions League final.
But the visitors had the best of a lively opening spell, with Mirko Vucinic and Jeremy Menez spurning good chances before Riise poked the ball into the far corner in the 21st minute after a lovely through ball from his captain Francesco Totti.
The European champions were struggling to muster a response when Vucinic gifted them a goal with a careless back pass into his own six-yard box, which Pandev pounced on four minutes before the break.
Roma also made the running at the start of the second half, with Menez volleying narrowly wide and Riise having a thunderbolt free-kick well saved.
But then Eto'o sneaked in ahead of the defensive cover to tuck away a cross from Diego Milito, who had just a goal disallowed for after a dubious offside call.
Eto'o sealed the victory by stealing possession outside the box, completing a one-two with Inter's Netherlands playmaker Wesley Sneijder and blasting home.
Brazilian forward Adriano, who walked out on Inter last year following problems with form, depression and discipline, made his competitive debut for Roma.
The match was suspended for about five minutes after Inter's second goal because Roma fans threw flares on to the field.
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