The Dutch side withstood fierce pressure in the remainder of the second half to hold out for all three points.
"Ajax came out more fired up and it wasn't easy for us. It was a different matter in the second half - we played more like what we expect from Barça," said Barca coach Tata Martino.
"In a Champions League game against a side who is playing for qualification to the knock out stage, you have to be full on for 90 minutes."
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