The Swans left it late to clinch all three points against Scunthorpe.
Despite dominating large chunks of the match it came to life inside the last five minutes when Scott Sinclair and substitute Stephen Dobbie sent the Liberty into raptures.
Sinclair opened the scoring while Dobbie completed a swift counter attack to double the lead less than two minutes later.
The result propelled Brendan Rodgers' side up to sixth in the Championship and extended their winning run at home to five in all competitions.
Swans: Dorus de Vries; Alan Tate, Garry Monk(C), Ashley Williams, Neil Taylor, Nathan Dyer (Albert Serran, 90+3'), Mark Gower, Joe Allen (David Cotterill, 76'), Scott Sinclair, Darren Pratley, Frank Nouble (Stephen Dobbie, 66').
Not Used:David Cornell (GK), Cedric van der Gun, Jordi Lopez, Jazz Richards.
Scunthorpe: Joe Murphy, Cliff Byrne (C), David Mirfin, Niall Canavan, Eddie Nolan, Josh Wright, Michael O'Connor, Sam Togwell (Bobby Grant, 86'), Michael Collins (Martyn Woolford, 67'), Jonathan Forte, Chris Dagnall (Rob Jones, 87').
Not Used: Sam Slocombe (GK), Andrew Wright, Michael Raynes, Matt Godden.
Attendance: 13,597 Away: 125
Referee: D McDermid (Hampshire)
The big news of the day was the decision to hand Frank Nouble his full debut just one day after the young striker arrived on loan from West Ham.
And that decision by manager Brendan Rodgers almost turned out fruitful as the 18-year-old came close to opening the scoring - with just 36 seconds on the clock.
Mark Gower's elegant chip over the defence found its way to Nathan Dyer, his cross into the area was half met by Nouble but, under pressure, was unable to steer his chance goalwards.
It was a strong start for the home side and, with the crowd finding their voice early on, they were back on their feet again four minutes later as Scott Sinclair glided past Cliff Byrne but saw his shot blocked.
Nouble was certainly looking to make a name for himself during the early stages, and with just 12 minutes gone he pounced on Michael Collins' back pass only to strike the side netting. The Londoner also won his new side a corner 60 seconds later, with Garry Monk heading onto the crossbar from Gower's resulting delivery.
But back came Scunthorpe, high as kites following their midweek demolition of Sheffield United, only to find themselves up against a stern home defence - Frank Nouble was even impressing at the back as he thwarted a counter attack by the Iron midway through the first-half.
In fact the Swans struggled to get the ball out of their own half at times, though Dorus de Vries wasn't forced into making any saves.
Joe Allen curled over and Dyer shot wide in the closing stages, while Michael Collins benefited from a Gower slip and charged down on goal, fortunately placing his shot to the right of de Vries' goal.
Half-Time: Swans 0 Scunthorpe 0
Frank Nouble used his pace to good effect at the start of the second period to win his side a free-kick in dangerous territory, and for a big man didn't look too bad with his feet.
Scott Sinclair curled the free-kick inches over the bar only to turn provider moments later, his cross floating over the Scunthorpe defence and falling for the unmarked Darren Pratley. And he came to within inches of adding to the goal he scored against Coventry when his volley deflected off goalkeeper Joe Murphy and onto the post, only for the Irishman to safely retrieve the ball afterwards.
Ash Williams sent a volley from Mark Gower's free-kick wide of goal just after the hour, and that was quickly followed by the Swans' first change of the afternoon as Stephen Dobbie was sent on in place of Nouble.
Gower tested Murphy from distance but denied the midfielder with a fine save, while the goalkeeper opened up his body to deflect a Scott Sinclair strike over top for a corner, and that came from a fine solo run which saw the ex-Chelsea youngster stride past three Iron players on 74 minutes.
The Swans continued to dominate the second period but, with 10 minutes left on the clock, Scunthorpe almost helped themselves to a goal as Sam Togwell completed a counter attack after finding space in the box - the midfielder struck it low but Dorus de Vries kept his balance to pull off an excellent save to deny him.
But normal service quickly resumed and within three minutes the hosts were in front - the ball pinged its way around inside the area with Scott Sinclair and Stephen Dobbie seeing their close-range headers half cleared, Nathan Dyer played it back into the mix and Sinclair was ideally placed to find the roof of the net.
And a frustrated afternoon in front of goal was put well and truly behind the hosts when they grabbed an immediate second; Alan Tate and Dyer worked well to feed Dobbie down the right, the striker charged down on goal and had players in space but, as he entered the area, pulled his shot across Murphy and found the net.
It almost opened up for Dyer to add a third in injury-time but the late double was enough to clinch maximum points and extend the Swans' winning run at the Liberty Stadium.