The former Queen of the South striker scored two second half goals to complete the victory after captain Garry Monk nodded home in the first period.
It could have been more with Mark Gower missing an open goal and Guillem Bauza spurning a good chance close to the end of the match.
Brighton's only real chance came before the interval when Tommy Elphick probably should have punished some slack marking inside the Swans bos, but managed to nod wide with de Vries stranded.
Paulo made five changes to the side that lost at Leicester on the weekend, with Fede Bessone, Matt Collins, Andrea Orlandi, Stephen Dobbie and Jordi Lopez all given a chance to impress.
Paulo named his side as follows:
Dorus
Collins Monk Tate Bessone
Dyer Britton Lopez Orlandi Gower
Dobbie
Early on, the Swans looked sharp and the passing was crisp, and put their League One opponents instantly on the backfoot.
Nathan Dyer was particularly impressive on the right wing and tore Jake Wright to pieces on a number of occasions before the Brighton man was substituted at half time.
In the 17th minute, the opening goal arrived, and it was that man Wright involved as he fouled Orlandi, who picked himself up to deliver the ball into the area which was nodded goalwards by Tate, and headed at home at the second attempt by Monk after the ball struck the woodwork.
It was no more than Sousa's men deserved for a dominant opening spell although moments later the visitors should have been level, Dean Cox sending a free-kick in to find Elphick completely unmarked, but he constrived to nod wide.
If Gower was starting to think he'd finally found some luck in a Swans shirt after an impressive pre-season goalfest, he was brought back down to earth with a terrible miss after another brilliant Dyer run found him at the back post.
Brighton, backed by a 100 or so away fans, started to hit back after the interval and showed some fighting spirit, but didn't really test Dorus too much thankfully.
Paulo's first change saw Jordi Lopez, who really struggled to get into his stride, leave the field for fellow countryman Guillem Bauza which saw Orlandi drop deeper into the midfield alongside Leon Britton.
It was Orlandi who created the second goal, he whipped a cross into the box which hit a Brighton defender and found Dobbie whose first time header was palmed away, but the Scottish striker was there to tap home the rebound on his full debut.
Russell Slade's men didn't give up and tried to go to a more attacking outlook, but Garry Monk and Alan Tate in the centre of defence did well to avert any threat posed by Glenn Murray and the veteran Nicky Forster.
Dobbie capped off an impressive evening by grabbing a third (I'm not sure he meant it, but all the same), clipping the ball past Michel Kuipers leaving him with the simple task of slipping it into an empty net.
It was comfortable, it was deserved and most importantly it was Paulo's first win as the new Swans boss, and gives everybody at the club – along with the fans – a boost ahead of the home clash against Middlesborough.
See you there!
