At least Elland Road manager Terry Venables was spared the embarrassment of witnessing the one-sided contest as he stayed at home with flu, leaving Eddie Gray in charge.
Dyer's goals were his first in the Premiership since April as Newcastle took their unbeaten run to eight games.
The easy victory was achieved after Bobby Robson made four changes from the side which defeated Bayer Leverkusen in midweek.
Shearer and Craig Bellamy returned to the attack in place of Shola Ameobi and Lomana LuaLua and Scotland Under-21 international Brian Kerr came in for Jermaine Jenas, who had suffered an Achilles injury in training, and Andy Griffin replaced the suspended Olivier Bernard.
Newcastle took a 17th minute lead with Dyer's first Premiership goal of the season. Bellamy's high centre was chested down by Shearer for Dyer to shoot past Paul Robinson from the edge of the six-yard box.
Harry Kewell should have equalised three minutes later but in taking the ball round Given he narrowed the angle and could only shoot straight at Griffin who was guarding the near post.
Leeds defender Michael Duberry headed close from a Jason Wilcox free kick, as strikers Alan Smith and Kewell lacked a cutting edge.
The home side replaced Wilcox with James Milner at the start of the second half but Newcastle took a firm grip with goals in the 48th and 56th minutes.
First Bellamy released Dyer to shoot into the bottom right corner, then Laurent Robert's free kick on the left was headed in by Shearer from six yards out.
Lucas Radebe's goalline clearance from Kerr's centre denied Newcastle a fourth goal and disgruntled Leeds fans reacted against chairman Peter Ridsdale - chanting "Ridsdale what's the score?".