Sheffield Wednesday set an unwanted club record of nine league games without a goal as Swansea strolled to a 4-0 Sky Bet Championship win.
Goncalo Franco swept Swansea into a 19th-minute lead before Zan Vipotnik enhanced his status as the Championship's top scorer with a second-half double.
Vipotnik blasted home a free-kick from the edge of the box before smartly finishing for his 15th league goal of the season, and 17th in all competitions.
Substitute Malick Yalcouye dribbled through two minutes from time to claim his first Swansea goal and secure the Welsh club's biggest victory of the season.
A sixth home win in seven league games moves Swansea up to 15th - their highest position since early November - and five points adrift of the play-off places.
While Swansea will hope to make a late-season push for the top six, Wednesday's fate is already sealed.
Distanced considerably from the rest of the Championship with 18 points docked after going into administration and then breaching EFL regulations over payment obligations, the Owls' total remains in the minus column.
Bailey Cadamarteri scored their last goal on Boxing Day and the young striker was sold to Wrexham on deadline day this week.
Failing to score in South Wales eclipsed the Owls' eight-game drought in March and April 1975, with Wednesday extending their barren run in front of goal to 14 hours of football.
Josh Tymon tested Murphy Cooper from 25 yards after seven minutes and Marko Stamenic fired wide before Wednesday's defence was breached.
Brazilian wingers Ronald and Gustavo Nunes, making his full debut after joining on loan from Brentford, were involved before Liam Cullen set up Tymon's teasing cross into the six-yard box.
Franco was on hand to slide home his fourth goal of the season and the Portuguese celebrated with a jig of joy with his Brazilian team-mates.
Swansea nearly doubled the lead when Vipotnik saw his snapshot deflected narrowly wide.
Wednesday had a sight of goal through Jarvis Thornton's wayward attempt, but it was pretty much one-way traffic with Tymon rustling the Owls' side netting.
Tymon's raids down the left had been a feature of the first half and he was close to a second goal contribution in first-half stoppage time.
The left-back spotted Cullen's clever run to the near post and the Wales international lifted his free-kick onto the crossbar.
Swansea's second goal was a matter of if, not when, as Nunes curled a shot straight at Cooper and Vipotnik headed wide another free-kick from Tymon.
The Slovenian striker was not discouraged, however, grabbing the ball after Yalcouye was upended after 70 minutes and beating Cooper with a ferocious free-kick above the goalkeeper's head.
Vipotnik finished from Ronald's cross nine minutes later before Yalcouye kept his composure to condemn Wednesday to their second-heaviest defeat of the campaign.
Swansea's Vitor Matos:
"What's most important is what I said since the first day - the squad has a lot of potential.
"We needed to make the squad the best possible team to compete. That's what we are still doing. That's what we are trying and this is what drives us.
"That's the championship this season as well. You win one game, you think you are close to the play-offs.
"You lose one game, you think you are close to the relegation.
"So being emotionally stable is quite important. That's what mindset we need to have."
Sheffield Wednesday's Henrik Pedersen:
"In training, we start to score goals. To bring it from the training to the match, it's still tough for them. But we are working on it.
"We are pressing with more players higher up when we want the ball. This is the most important message I gave to the players before we went to the pitch.
"Go out and express yourself. Go out and when you are one with one, take this risk to bring extra man into the box. I know it will be there."
