Craig Beattie and Cedric van der Gun were on target as the Swans registered their first win at Scunthorpe for over 10 years.
Front-man Beattie hit his third goal in his last three away games with a well-struck free-kick just after the half-hour mark after Joe Allen came close to scoring his first of the season.
The home side rarely threatened in the first period but enjoyed spells of pressure early in the second-half, but were undone by a counter attacking Swans move.
Cedric van der Gun played a neat one-two with Darren Pratley before racing into the area and firing low beyond Joe Murphy to wrap up the win.
Joe Allen and Garry Monk both returned to the Swans' starting line-up for this match at Scunthorpe.
Youngster Allen started only his third game of the campaign while Monk was back after shaking off the calf injury which has ruled him out for the past three games.
Albert Serran also made the bench for the first time this campaign but both David Cornell and Jazz Richards were on international duty with Wales at Under-19 level.
The hosts were without influential defender Rob Jones (back) while Wolves loanee George Friend, who only joined on Friday, was on the bench.
Scunthorpe: Joe Murphy, Marcus Williams, Sam Togwell, Cliff Byrne (C), Grant McCann (Matt Sparrow, 57'), Paul Hayes (Garry Thompson, 74'), Gary Hooper, David Mirfin, Michael O'Connor, Josh Wright (Martyn Woolford, 57'), Niall Canavan.
Not Used: Sam Slocombe (GK), Jonathan Forte, Jordan Spence, George Friend.
Swans: Dorus de Vries; Angel Rangel, Ashley Williams, Garry Monk(C), Alan Tate; Joe Allen (Jordi Lopez, 67'), Leon Britton, Darren Pratley, Cedric van der Gun, Mark Gower (Tom Butler, 39'); Craig Beattie (Gorka Pintado, 74').
Not Used: Nathan Dyer, Lee Trundle, Fede Bessone, Albert Serran.
Attendance: 5,201 Away: 314
Referee: K Evans (Lancashire)
The sun was beating down at Glanford Park and despite the home bursting from the blocks it was the visitors that enjoyed the better start.
After robbing Grant McCann of possession in midfield Leon Britton sent Craig Beattie on his way into the Scunthorpe half, the club's record signing played into the path of Joe Allen inside the area but the ball was played a little too quick in front of him.
The Wales international had the game's first attempt at goal minutes later, latching on to the end of Angel Rangel's byline cross but from 12-yards sent the ball high into the terrace behind.
Gary Hooper offered the Iron's first attacking threat when he broke into Dorus de Vries' area only to be outmuscled by Ashley Williams, while Beattie fired inches past Joe Murphy's post with a well struck shot 30-yards from goal with 11 minutes played.
The Swans were dominating early possession and as the game reached the 15th minute both Beattie and Pratley were handed half chances, the latter failing to connect with Allen's cross-box pass on the edge of the area.
Ashley Williams made a fine defensive block to deny skipper delivering a right-sided cross, forcing a corner, while Beattie fired another chance past Murphy's right-hand post on 20 minutes, this time from 20-yards out.
Paulo's side were enjoying the majority of play and offered threats from corners and set-pieces before making a chance count from a free-kick with 32 minutes played.
Sam Togwell grounded Darren Pratley 25-yards from goal, Britton and Beattie both stood over the ball but it was the latter who struck it low and it rifled under the wall and into the bottom corner of the net.
That was his third in his last four starts and within two minutes of breaking the deadlock he almost made it four in four when the Scot received the ball from Cedric van der Gun 18-yards from goal but this time failed to hit the target.
Paulo made his first change six minutes before the break as Tom Butler replaced Mark Gower out wide, for what looked like an injury, and his first duty was to deliver a corner from the right.
Alan Tate's came inches close to heading his delivery goalwards while another low cross from the Irishman was cleared from under the cross bar by Cliff Byrne.
Scunthorpe rarely threatened during the first period but a wicked half volley on the stroke of half-time by Michael O'Connor, which was easily dealt with by de Vries, was their first attempt on target.
Half-Time: Scunthorpe 0 Swans 1
It was as you were after the restart and with just 65 seconds played the Swans looked to add to their tally when Beattie forced a fine save from Murphy who pushed the ball wide for a corner.
Scunthorpe replied with Paul Hayes firing across goal and past the post while Michael O'Connor saw his half volley blocked and cleared by the visitors' defence.
Nigel Adkins' side enjoyed a brief spell of pressure but nothing was conjured up in order to trouble Dorus de Vries between the Swansea sticks.
The hosts made two changes, bringing on Woolford and Sparrow, and the former looked lively down the left-hand side as he linked up with left-back Marcus Williams.
But against the run of play 22 minutes into the second period the Swans added a second - Cedric van der Gun and Darren Pratley playing a neat one-two on right hand side, that enabled the Dutchman to race into the area and fire low beyond Murphy and give his side the edge.
Before play resumed the Swans made their second change of the afternoon when Jordi Lopez replaced the tireless Joe Allen in midfield, while Gorka Pintado was introduced shortly afterwards in place of opening goalscorer Craig Beattie.
There was a slight concern surrounding Darren Pratley when he went down under a challenge on the edge of his own area, but after a moment of treatment from Cerian Parham he was able to walk off before continuing.
With five minutes left on the clock Pintado had the chance to make the points safe when he was played through by Darren Pratley only to be denied by David Mirfin's last ditch tackle.
Martyn Woolford fired over as time was running out but the Swans stayed strong to make it nine games unbeaten.