Real Madrid coach Pellegrini heaps praise on Higuain after hat-trick
Raul Albiol's own goal, which briefly reduced the arrears to 3-1, was all the home side could muster.
Wednesday night's 1-1 draw with Lyon at the Bernabeu, which gave the French side a 2-1 aggregate win in their Champions League last-16 tie, had called into question the position of coach Manuel Pellegrini.
But, with Barca having piled the pressure on even more with a 3-0 win over Valencia earlier in the evening, his side never looked in danger of suffering further embarrassment against a side battling desperately against relegation.
Pellegrini said afterwards: "I'm happy with how the team responded but there are many shortcomings to be corrected but we are increasing our football and scoring ability. We now have seven or eight wins scoring more than three goals. Today we scored four in a venue that in the past had not been favourable.
"He was concerned during the week but has a great character. He is unfairly accused of missing a goal and of selfish behavior. He has had the same feeling as anyone. We are all hurt."