Tammy Abraham scored twice as Swansea registered their first three points at home this season with a 2-0 victory over Huddersfield.
Though they started the brighter, the Swans allowed their opponents space to play for much of the first half until they took the lead when Abraham slotted home Tom Carroll's cut-back after Jonas Lossl's poor clearance (42).
Australia international Aaron Mooy was introduced for the second half, but he inadvertently set up Swansea's second when he dispossessed Luciano Narsingh and the ball fell to Jordan Ayew, with Abraham ensuring the Ghanaian's dink crossed the line (48).
The result means Swansea now sit 13th in the Premier League standings, just a point behind the Terriers, who continue their slide down the table.
Home Team: Fabianski (5), Naughton (6), Fernandez (5), Mawson (6), Olsson (6), Fer (7), Britton (6), Carroll (7), Narsingh (6), Ayew (7), Abraham (8)
Subs: Dyer (4), Ki (5), Clucas (N/A)
Away Team: Lossl (4), Smith (5), Jorgensen (4), Schindler (6), Malone (5), Billing (5), Hogg (6), Kachunga (6), Van La Parra (6), Ince (5), Depoitre (4)
Subs: Mooy (6), Lowe (N/A), Williams (4)
Man of the match: Tammy Abraham
Swansea flew out of the blocks in the first top-flight meeting between the pair and looked like they might catch the Terriers out early on with a number of bright forays down the right flank.
But Huddersfield grew into the game after being initially startled and though Tom Ince blazed over, he had a great chance to open the scoring when he met Rajiv van La Parra's teasing cross from the left after 27 minutes.
Referee Paul Tierney had a vital call to make four minutes later when Ince appeared to be brought down inside the area by Martin Olsson as he raced onto a lengthy delivery from Lossl, but the visitors' appeals were immediately waved away.
Paul Clement's men held off their opponents as the half progressed, but capitalised on a mistake from goalkeeper Lossl to take the lead - against the run of play - through Abraham three minutes before half-time.
Swansea pair Wilfried Bony (hamstring) and Renato Sanches (thigh) both picked up injuries on international duty and were replaced by Leroy Fer and Luciano Narsingh. Scott Malone made his first Premier League start in place of Chris Lowe, while Aaron Mooy settled for a place on the bench following his exploits in Australia's World Cup play-off win against Syria in midweek.
A poor delivery in the direction of Mathias Jorgensen was intercepted by Carroll, who cut the ball back into the area towards Ayew, whose dummy gave Abraham the opportunity to slot home his third league goal of the season.
Wagner introduced his trump card - Mooy - at the break, but despite an energetic start to the half, it was the Australian who unintentionally created the second three minutes after the break.
Tracking back the length of the pitch, Mooy made an important challenge to dispossess Narsingh but the ball fell to the feet of Ayew, who chipped over Lossl, leaving Abraham to tap in for claim Swansea's second.
The returning Ki Sung-yeung almost made it three when he shifted his weight and arrowed a low shot just wide of Lossl's post and the day got better for Swans fans as Nathan Dyer made his comeback from an Achilles injury that had sidelined him since February.
But there was no way back into the game for Huddersfield, who have now scored just one goal in their last six and are without a win since August 20.
Paul Clement: "It was a very important game, we knew that after the start that we've had and particularly with the start we've had at home. So we wanted to put a good performance in today for our supporters who really got behind the team.
"I'm most pleased about the performance that the players put in. We've been defending reasonably well and that's four clean sheets out of eight which is a good standard. But we hadn't really hit the ground running with our offensive play.
"We got our first goal from some misfortune but that came from our aggressive pressurising which we did throughout the game. It wasn't luck because we studied Huddersfield in lots of detail. They are a team who play out from the back and there is a certain risk associated with that and we practiced those situations. It didn't happen in the first 42-43 minutes, but we kept at it and I have to say that we forced that error.
David Wagner: "First half [we were] not good enough, not brave enough - I think bravery was a big problem for us in the first half. And, as everybody has seen, there were a lot of situations against us - the Tom Ince situation where it could be a penalty or a free-kick. I think you could [blow the] whistle, I've seen red cards for these situations.
"We had probably biggest chance in the first half from Tom Ince as well. We were not brave enough in the first half and we didn't have the luck in the second. I think we created moments, we hit the bar and had a number of dangerous situations in the six yard box, but unfortunately we were not able to score.
"I think it was a great tackle from Aaron Mooy, but unfortunately he tackled the ball into Ayew's feet - it was a very good finish. But this is exactly the situations that I meant - you have to invest in bravery if you like to be lucky."
Man of the match - Tammy Abraham
Two real poacher's chances grabbed by the scruff of the neck and converted by Tammy Abraham today. In the right place at the right time on both occasions, the Chelsea youngster impressed as he took his league tally to four.
The striker put his defensive qualities on show a number of times, too and once again proved that he can cope with the step up from the Championship with his maiden Premier League brace. A real asset to Paul Clement.
The pundit - Phil Thompson
"I like people playing football but you don't take risks; the ball has come back to Lossl and he's tried to side-foot it out. There hadn't been a great deal in the match at that point but probably Swansea had been the best. It's such a downer for Huddersfield and at this moment in time, they can do without that.
"They did have a couple of chances through Ince and Van La Parra but other than that Lukasz Fabianski didn't have a lot to do.
"It was a thoroughly deserved win by Swansea, with some good players all round. Abraham did nick the goal, but I think he's right to do that - he's a poacher."
- Swansea have enjoyed consecutive league wins over Huddersfield for the first time since August 1993, and after drawing one and losing five of the previous six.
- Huddersfield have failed to score in four consecutive games in all competitions for the first time since August 2004.
- Abraham scored as many goals against Huddersfield (2) as he had in his previous nine league games.
- Carroll registered his first Premier League assist in 19 games, since March (v Burnley).
- Since his debut for Swansea in February, Jordan Ayew has been directly involved in more Premier League goals than any other current Swans player (2 goals, 4 assists).
- The Terriers are without a win in six league games (D3 L3) for the first time since November 2015.
- Swansea enjoyed their first top-flight win in five games, and have scored exactly two goals in each of their last four Premier League victories.
Craig Shakespeare's Leicester City are next up for the Swans as they welcome the Foxes to South Wales in a week's time, while Huddersfield have the daunting task of hosting Jose Mourinho's rampant Manchester United.