Eddie Howe's men had been second best in a first half which saw Chris O'Grady and then Steve Dawson rattle the same post for a Barnsley side who are yet to take even a point on their travels this season.
But inspired by the introduction of record signing Tokelo Rantie, the home side upped the ante and after Lewis Grabban uncharacteristically missed a simple chance Pugh lashed the ball home with his weaker foot to seal the points.
Barnsley boss David Flitcroft made four changes to the team narrowly beaten by Nottingham Forest on Saturday with Luke Steele, Chris Dagnall, former Cherry Martin Crainie and Tomasz Cywka all earning starts while Bournemouth remained unchanged.
Rantie, who only arrived in the country on Sunday, had to make do with a place on the bench as Howe stuck with top scorer Grabban and the striker had two early sniffs at goal.
Winger Ryan Fraser, one of their impressive performers in Saturday's loss to Blackpool, provided a delivery from the right wing which Grabban could only head straight at Steele.
Eight minutes later Peter Ramage's perfectly timed block denied Grabban as he prepared to pull the trigger.
In a half of very few clear cut openings at goal Barnsley had the two best opportunities to break the deadlock within a second.
First O'Grady's drilled strike across goal from the left-hand side cannoned off the inside of the far post. It fell straight to Dawson who could only return the ball to exactly the same spot of a relieved Ryan Allsop's left-hand post.
The Tykes, searching for their first three-point haul on the road since February 9, were enjoying their best spell of the half and were restricting their hosts to half chances.
Cywka scored a stunning goal from range on Saturday and he was inches away from adding his second memorable strike in four days before Dagnall drilled a right-footed volley wide minutes later.
But just 60 seconds into the second half Bournemouth really should have taken the lead when the usually reliable Grabban somehow fired wide after being sent one-on-one inside the penalty area by Pitman.
It took just 10 minutes of the second half for Howe to turn to Rantie, who arrived from Malmo last week, a decision which delighted the home fans.
And he was so close to making the perfect start to his life on the south coast within a minute of his introduction when the South African twisted and turned past his marker before bending a low shot just inches past the post.
Bournemouth, yet to draw a match this season, were beginning to up the ante with Elliott Ward's fizzing half-volley flying wide, Grabban heading Simon Francis cross' into the arms of Steele and Pitman's snapshot being scrambled behind by the keeper and several defenders.
Having scored in every league game this season the Cherries faithful sensed a Bournemouth goal was coming and it duly arrived in the 76th minute when the ball was pulled back to Pugh, who sidestepped his marker and drilled a low left-footed shot into the back of the net.
Rantie and Pitman both missed late chances as Bournemouth's fourth win of the season moved them to within four points of the top of the table.