In what was a clash of cultures in Wales, Russell Martin's side played their possession-based game while Valerien Ismael's side looked to counter-press with energy and aggression.
The Baggies got off to a dream start when, after winning the ball high, Karlan Grant put them ahead after just 52 seconds.
But it was the hosts who were by far the better of the two teams after the break.
Joel Piroe pulled them level just past the hour mark after beating the offside trap.
And then in the 83rd minute, Jamie Paterson won it with a brilliant individual goal following a mistake from Darnell Furlong.
Boss Ismael made one change from the team that secured the derby bragging rights by beating Blues last Friday.
With Alex Mowatt suffering a recurrence of a foot injury in that game, Jayson Molumby made his first Baggies start in central midfield.
In Ismael's 3-4-3 formation, he lined up in the middle of the park alongside skipper Jake Livermore with Darnell Furlong and Conor Townsend the wing-backs.
Up front, Callum Robinson continued as Albion's central striker with Matt Phillips on the right flank and Grant on the left.
Swansea, fresh from thrashing rivals Cardiff on Sunday, lined up in a 3-4-2-1 formation.
Joel Piroe was their lone striker with Korey Smith and Jamie Paterson operating just behind.
In his brief time as a manager, Martin has become known for his possession-based philosophy which sees his team play out from the back at almost every opportunity.
And their reluctance to clear their lines caught them out inside the opening minute when two poor passes deep in their own half allowed Livermore to win the ball high.
The ball was then worked to Robinson who sent in a low cross which Grant gladly tapped home with just 52 seconds on the clock.
After that blistering start, the game settled into the pattern that was expected before kick-off with the hosts looking to keep the ball down and move it through the thirds.
Albion, though, were playing with such tenacity and aggression that they continued to be the more dangerous of the two sides.
And they came close to doubling their lead when a dangerous free-kick from Phillips was only half-cleared.
Livermore pounced on the loose ball but from eight yards he fired high and wide when he should have done better.
As the clock ticked past the half-hour mark, Martin's side began to look a bit more dangerous - with Piroe hitting the byline before seeing a dangerous low cross cleared by Furlong.
Overall, though, they had created very little despite having enjoyed 72 per cent possession.
And it was Albion who created the final chance of the half with Phillips charging into the box before hitting a low drive that was saved by Ben Hamer.
Swansea made a change at the interval with Olivier Ntcham replacing Flynn Downes in midfield.
Albion started the second half on the front foot with Matt Clarke heading a Furlong cross wide before Livermore hit a low drive from 20 yards which Hamer parried away.
Swansea responded with Ntcham meeting a crossfield ball into the box at the back post but volleying wide.
Time and time again the hosts were being caught offside when they looked to switch the play with Martin and his bench furious they kept being on the wrong side of a number of tight calls.
But you couldn't help but feel, eventually, one of those decisions would go their way.
And so it proved just past the hour mark when a ball over the top put Piroe through on goal with Albion's defenders appealing for a flag.
That flag, though, never came with the Dutch striker then doing well to hold off Clarke before firing past Sam Johnstone and into the net.
Now with their tails up, the Swans went close just minutes later with Ntcham hitting a strike from the edge of the box that sailed inches wide.
Albion were suddenly coming under quite a bit of pressure.
But, against the run of play, they almost got themselves back in front when Phillips hit a fierce drive from 25-yard which Hamer touched onto the crossbar.
With 10 minutes to go the game had become more open with there a feeling inside the stadium that either side could win it.
But it was the hosts who went on to snatch all three points with a goal all of Albion's making.
After Livermore spread the play, a dreadful touch from Furlong presented the ball to Paterson who charged into the box before brilliantly tricking his way past Bartley.
And the former Walsall man then kept his composure to slot the ball past Johnstone and into the corner of the net.
Swansea (3-4-2-1): Hamer, Bennett, Naughton, Cabango (Williams 86), Laird, Grimes, Downes (Ntcham 46), Bidwell (Latibeaudiere 86), Paterson, Smith, Piroe.
Subs not used: Benda, Whittaker, Cullen, Walsh.
Albion (3-4-3): Johnstone, Ajayi, Bartley, Clarke, Furlong, Livermore, Molumby (Snodgrass 79), Townsend, Phillips Reach 84), Robinson (Hugill 56), Grant.
Subs: Button, Bryan, Kipre, Gardner-Hickman.