Zinedine Zidane's side, comfortable 3-1 first-leg winners on Sunday, put Cristiano Ronaldo's five-game ban behind them by out-playing their arch-rivals again as moments of magic from Asensio and Benzema put them out of sight.
Asensio's superb, swerving early strike set the tone at the Bernabeu and Benzema added a second six minutes before half-time to leave a dispirited Barca staring at a heavy defeat.
Ernesto Valverde's side improved in the second period, with both Lionel Messi and Luis Suarez seeing efforts hit the woodwork, but Real were by then in cruise control.
It means that the two powerhouses of football in Spain head into the new LaLiga season with Real Madrid 4/5 favourites at Sky Bet just ahead of Barcelona at even money.
Madrid pair Gareth Bale and Isco, star of the show at Camp Nou three days ago, were left on the bench, while Barca were without injured captain Andres Iniesta and his absence clearly told.
Barca found themselves behind in the fourth minute when Asensio followed up his fine goal in the first leg by slamming home a left-footed shot from 30 yards, which left goalkeeper Marc-Andre ter Stegen stranded.
Messi had been anonymous for the first 16 minutes, but briefly threatened with brilliant footwork in the box and then his ball across the face of goal eluded Luis Suarez.
Asensio had another shot blocked after combining with Benzema and Toni Kroos fired wide before Lucas Vazquez almost made it 2-0 on the night when his curling shot hit the crossbar.
But Real did get a deserved second when Benzema pounced ahead of flat-footed Real defender Samuel Umtiti in the 39th minute and turned sharply to fire home a low shot into the bottom corner.
Vasquez fired straight at Ter Stegn and Benzem rifled over the crossbar as Real looked set to add to their score.
Messi burst into life again in the 53rd minute, dancing past two defenders to crash an angled shot against the crossbar and although Barca improved after the break they still lacked real cohesion.
Suarez's diving header came back off the outside of a post after Real goalkeeper Keylor Navas had parried Messi's stinging drive in the 71st minute and Ivan Rakitic's effort was blocked.
But Real had visibly eased off. Asensio and Kroos were both withdrawn and Los Blancos were content to sit back and repel Barca's ponderous forays forward.
