Boro came into the game having not scored a goal in three matches and they did not manage a shot on target in a first half totally dominated by Graham Potter's free-flowing Swansea side.
With Bersant Celina orchestrating things brilliantly from midfield, and the dangerous Dan James and Nathan Dyer causing plenty of problems on the flanks, the home side built on their 3-0 home win against Brentford earlier in the week to score two goals before the break.
They enjoyed 69 per cent of possession in the first half but it took them more than half an hour to break down a stubborn Boro defence that set out to frustrate a side that started the day eight points and six places beneath them.
Pulis' men found themselves immediately on the back foot and were pleased to see Celina volley over the top of their goal after Wayne Routledge had set Dyer free down the right.
James then cut in from the left edge of the box and thundered a 30-yard shot just wide of the post, before Routledge hit the crossbar after a great build-up between him and Celina.
It was Wales winger James who helped to break the deadlock when he won a penalty after 34 minutes. The 21-year-old raced into the box only to be brought down by Daniel Ayala, allowing Matt Grimes to hammer home his first league goal of the season.
That gave Swansea renewed confidence and four minutes later they made it 2-0 as they once again broke out from their own half. Celina picked up the ball and drove forward before releasing Routledge.
The attacker put one defender on his backside as he controlled the ball on the edge of the area and then picked his spot in the bottom left corner to bag his third goal of the campaign. James almost made it three after a high-speed break over 80 yards, but his curling shot whistled past the post.
Boro skipper for the day, Stewart Downing, nearly had something to celebrate on his 400th appearance for the club when he shot inches wide six minutes after the break. That was the closest they had come, but they then found themselves falling further behind.
Dyer and Celina combined down the left and it was the Kosovan's cross that allowed Connor Roberts to slide in on the far post in the 71st minute and beat Darren Randolph for the second three-goal haul of the week for the Swans.
The Boro goal drought finally ended after six hours and 49 minutes when George Saville scored in the 81st minute from a Downing corner.