Maybe it was the five days in Marbella that did the trick. Fresh from some welcome winter sunshine during the international break, Huddersfield Town achieved their first away win of the season, courtesy of two goals from Aaron Mooy, to climb six places in the table.

Bottom of the league at the start of the day, David Wagner’s side departed the Black Country in the relative comfort of 14th place after outplaying Wolves, who were booed off by the home fans at the interval and again at full time.

It was the first time Huddersfield have scored more than one goal in a Premier League game since February – a run of 23 fixtures – and it is a measure of how well they played here that they could easily have scored three or four. “We hope we can continue to surf this wave,” Wagner said.

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Wolves, in contrast, were awful, totally unrecognisable from the team that have taken points off Manchester City, Manchester United and Arsenal this season. Perhaps most worryingly of all for their manager, they looked beaten from the moment that Mooy scored after six minutes. “The beginning of the game we felt we were never going to change the course of things,” Nuno Espírito Santo said.

Huddersfield, in short, thoroughly deserved their victory on an afternoon when Wagner got his tactics spot on. The visitors outnumbered Wolves in central midfield, denying Rúben Neves and João Moutinho the time and space to get control of the game, and in Philip Billing they had the outstanding player on the pitch.

A dynamic and effervescent presence, Billing must have covered almost every blade of grass and, crucially, made a superb goalline clearance to deny Raúl Jiménez an equaliser. “That was at least as important as a goal,” Wagner said. “Phil is a man now. He’s got this little bit of fighting spirit in his game which we always missed. He’s got the technique and the vision, he’s 6ft 6in, he has a throw-in and unbelievable shot – he has everything. He’s a very, very big talent.”

Facebook Twitter Pinterest Aaron Mooy, left, sidefoots Huddersfield into a lead at Molineux. Photograph: Andrew Yates/Reuters

Although Billing’s clearance was a turning point in the game, it says everything that Nuno never even mentioned that moment afterwards. The Wolves manager looked and sounded every bit as exasperated as the supporters whose groans got louder and louder with every misplaced pass – and there were plenty of them.

“Disappointing for us and our fans who deserved a better performance. Today we were very bad, and when you play bad you lose,” Nuno said. Asked what the reasons were for such a listless display, he added: “This is a job that I have to do this week, try to find out why. Everybody made mistakes. We didn’t have the ball. When we had it we lost it, we rushed ourselves, we were not compact; too far away from each other. A bad game. But credit to Huddersfield, I think they pressed us very well and deserved to win.”

Huddersfield’s breakthrough turned out to be a sign of things to come as Billing released the overlapping Erik Durm, who intelligently picked out Mooy. Totally unmarked on the edge of the area, Mooy expertly steered a low shot into the bottom corner with his right boot. It was a lovely finish, and Steve Mounié should have added to it before half-time.

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The introduction of Adama Traoré added some pace to the Wolves attack in the second half and it was the substitute’s cross that Jiménez headed past Jonas Lössl, Huddersfield’s goalkeeper, only for Billing to come to the rescue. As the game became stretched, Jiménez made a pig’s ear of another chance and Rui Patrício denied Alex Pritchard at the other end before Mooy sealed victory with a perfectly executed free-kick.

Spotting a gap inside the near post, the Australian curled the ball around the outside of the wall and beyond Rui Patrício’s despairing dive to propel Huddersfield up the table.

“We’ve known we are not as poor as maybe everybody thinks, because we have seen and played the games,” Wagner said. “This time it was different and I am very happy that the players got their reward.”