The result sees Napoli advance in the competition.
"We knew that it was going to be an important and difficult match," Higuain told Mediaset.
"Swansea forced us to wait until the 70th minute before taking the lead. I want to thank my team and our fans for helping us to achieve this qualification.
"We had started the game well, but after the equaliser we lost our way. We can consider ourselves satisfied with the result.
"My goal was more important than it was beautiful, but that still makes me happy."
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