In addition, Southampton's win in Wales left Swansea three points adrift of safety and simultaneously relegated West Bromwich Albion.
Hughes, who took the Saints reins on March 14, was relieved with his side's victory in the relegation six-pointer but is not ready to celebrate survival just yet.
"It was a big performance from us," the Welshman told BBC Sport. "I came in late to proceedings and needed to get a reaction our of players who had maybe lost their way somewhat. I have to say, since I've come in they've worked hard and even when results when against us never diminished belief.
"It is not mathematically certain. We had to come here and we had to win. If we had not won today it would have been very, very difficult for us. It is not done yet but tonight we have put ourselves in the position where we have a great chance to stay up.
"We will enjoy tonight, we got what we set out to get. A huge result, we are delighted but still got work to do."
Southampton's final game of the season is at home to Manchester City on Sunday.