The Swans hit the 60 point mark for the season with this stalemate against Sheffield Wednesday.
Paulo's side tested Lee Grant in both halves but the visiting 'keeper was at hand to make some good saves; but Darren Pratley, substitute Shefki Kuqi and Ashley Williams - with a last minute header - all came close in the second period but just couldn't hit the target.
The one point gained opened up a gap of 10 between the Swans and Blackpool in seventh spot ahead of the next clash against high-fliers West Brom on Tuesday.
Swansea City were handed a huge boost with the return of David Cotterill from injury.
The Wales international winger had missed the last two outings against Nottingham Forest and Watford with a hamstring problem but returned to the starting eleven for this game.
Cedric van der Gun and Shefki Kuqi dropped to the bench in place of Cotterill and Tom Butler, while there was also a return from an ankle injury for Nathan Dyer who was named amongst the substitutes.
Swans:Dorus de Vries; Angel Rangel. Alan Tate(C), Ashley Williams, Jazz Richards; Leon Britton, Mark Gower, Darren Pratley, David Cotterill (Lee Trundle, 77'), Tom Butler (Cedric van der Gun, 46'); Craig Beattie (Shefki Kuqi, 46').
Not Used:David Cornell (GK), Guillem Bauza, Nathan Dyer, Lee Lucas.
Owls: Lee Grant, Eddie Nolan, Darren Purse (C), Mark Beevers, Tommy Spurr; Tommy Miller, Darren Potter, James O'Connor, Jermaine Johnson; Leon Clarke, Luke Varney (Marcus Tudgay, 71').
Not Used: Richard O'Donnell (GK), Richard Hinds, Etienne Esajas, Frank Simek, Tom Soares, Michael Gray.
David Cotterill was playing in his first fixture since scoring the winner against Peterborough at the Liberty two weeks earlier and he was showing no signs of the hamstring injury that's kept him out.
He was running at Owls' right-back Eddie Nolan from the first whistle and even tried his luck from distance with just four minutes on the clock, a dipping shot which 'keeper Lee Grant misjudged its trajectory but was able to claw the ball from underneath the crossbar.
His opposite number, Dorus de Vries, was forced into making a similar stop two minutes later by stopping a Leon Clarke strike from 20-yards on the line.
Both sides kept seeing possession of the ball inside the first quarter of an hour but Darren Pratley, whose pre-Christmas double sunk the Owls at Hillsborough, almost added to his seasons tally with a shot from outside the box with 13 minutes played which was dealt with by Grant.
The midfielder played a part in the Swans' next attempt at goal five minutes later as he raced into the right-hand corner before threading Tom Butler to the by-line; the Irish wide-man delivered a first-time cross which picked out Beattie eight-yards from goal but the former West Brom man failed to hit the target with a header.
The first quarter of this contest passed with little goalmouth action - especially at Swansea's end - but Jermaine Johnson came close with their best effort of the afternoon so far with an angled strike which deflected inches over the top of goal.
That was just before the half-hour and the Swans went straight down to the other end where former Sheffield United man David Cotterill rode the challenges of two players before an unleashing a low, powerful drive which Grant collected.
Both sides pressed for an opener but it just didn't come at the end of what was a disappointing opening period.
Half-Time: Swans 0 Owls 0
Cedric van der Gun and Tuesday's goal hero Shefki Kuqi were introduced at the break and within three minutes the latter came close to scoring his second in four days.
Darren Pratley chased down Alan Tate's through ball to the byline where Tommy Spurr looked to shepherd it out, but the midfielder hooked his foot around the ball and delivered it to the edge of the box where Kuqi was placed to send a fierce volley inches past the post.
Fellow sub van der Gun also got in on the action four minutes later with a surging run into the area, following a neat one-two with Kuqi, only for Grant to collect at the Dutchman's feet.
The visitors enjoyed a short spell of pressure before the hour but failed to test de Vries; Mark Gower saw a shot blocked before the best chance of the half so far fell to Pratley who, from four-yards, connected with van der Gun's right-sided cross only to send it over the top of goal.
Wedesday were handed a chance from a free-kick which was dealt with by Swansea' defence, the ball picking out Cotterill wide left and he used his pace to run at the defence, cut inside and forced Grant into making a fine save on 69 minutes.
Lee Trundle was thrown on as Paulo's last throw of the dice in place of Cotterill and he had a chance to break the deadlock five minutes from the end when he was played into the area by Mark Gower, taking a touch before pulling his low effort past Grant but also past the foot of his far post.
Ashley Williams came agonisinly close to claiming a dramatic winner right on the stroke of full-time as his header from Gower's cross fell inches the wrong side of the post, and as the Swans support were still coming to terms with what they thought was an opener the fourth official indicated that seven minutes of injury-time was still to be played.
And it was in the final minute of that added time that the Swans came closest to claiming maximum points - a long punt downfield falling at Trundle's feet, he cut inside his man but, from the edge of the area, curled a left-footed strike over the top of goal.