Premier League: Newcastle 1 Swansea 2
The Magpies failed to capitalise on a number of opportunities on goal, with second-half goals from Michu and Jonathan de Guzman enough to seal all three points for the Welsh outfit, who leapfrog Alan Pardew's side in the table.
Pablo Hernandez carved out the first chance of the game within five minutes.
The former Valencia man's through ball split the Newcastle centre-backs to play Dyer in on goal, yet the 24-year-old dragged his effort wide of Tim Krul's goalmouth.
The Dutchman was then on hand to thwart the midfielder's own attempt from distance.
The lively Hatem Ben Arfa had an effort that crashed against the side netting following a mazy run, yet the visitors continued to look the more threatening and only a brilliant save from Krul prevented Michu from opening the scoring.
The Frenchman was then on hand to tee up Demba Ba with a driven cross from distance. Yet the Senegalese striker, limited to long-ball service for much of the half, was unable to direct his header on goal.
Up popped Ben Arfa again to force a superb save from Gerhard Tremmel in the Swansea goal before Itay Shechter failed to guide the ball beyond Krul as the half ended goalless.
The introduction of Shola Ameobi after the break in place of Shane Ferguson gave Newcastle added impetus, with the striker teeing up Vurnon Anita to drive at goal from distance.
The hosts continued to pile on the pressure, with Ba gifted two opportunities in quick succession, but the striker failed to threaten on both occasions.
However, a poor Krul clearance gifted Laudrup's men an opportunity on the break, and the Dutchman was made to pay.
Hernandez picked up the ball on the halfway line, and drove down the flank before teeing up Michu to head Swansea into a deserved lead.
The home crowd's frustrations were increased as Newcastle continued to prove wasteful in the final third - Sammy Ameobi a major culprit - while Swansea looked increasingly likely to score a second.
The visitors soon wrapped up the points with de Guzman the first to pounce on a rebound from a Krul save and drive the ball home from a tight angle.
Newcastle may have hoped to have salvaged a point after Ba's late header, but their stuttering start to the season continues.