Madrid made the brighter start of the two sides, as Higuain forced Barca goalkeeper Victor Valdes into making a good save from just 10 yards in the sixth minute.
Five minutes later the Argentina international striker redeemed himself for Madrid when he found the target from close range, after Javier Mascherano was caught out by a long ball over the top.
It became 2-0 to Madrid in the 19th minute when Cristiano Ronaldo flicked a long ball over Gerard Pique with an astonishing back heel and put it past Valdes with ease from inside the penalty area.
Madrid thought that they had scored their third goal of the evening in the 23rd minute when Pepe headed a free kick into the Barca net, but it was ruled out for offside.
Things turned from bad to worse for Tito Vilanova's side on 28 minutes when Adriano was sent off after pulling down Ronaldo when the Portuguese forward was through on goal.
Jose Mourinho's men continued to dominate proceedings and test the Barcelona defence, but conceded on the stroke of half-time.
Barcelona won the first leg 3-2 at the Nou Camp last week.