Without the injured Alan Shearer, Dyer was thrust up front and responded with the only goal to make it three wins out of three for caretaker boss Glenn Roeder who can surely be doing his chances no harm of getting the job on a permanent basis.
In their 350th FA Cup tie, the six-time winners - who have reached 13 finals - maintained their proud unbeaten home Cup record stretching back to 1997.
United have yet to concede a goal in the competition this season though they rode their luck against Southampton.
The two sides had met on seven previous occasions in the FA Cup with the balance of power firmly with the Saints who came out on top in the first six of those meetings.
Newcastle won the last of these showdowns 3-0 in the third round two years ago with Dyer twice on target on that occasion.
United had a good early chance when Charles N'Zogbia's ball from the left was missed by Shola Ameobi and Nobby Solano crashed in a shot from an acute angle that Bartosz Bialkowski got away.
A wayward Jean-Alain Boumsong cross saw central defensive colleague Titus Bramble come to his rescue, but from Jim Brennan's cross Kenwyne Jones got up well only to glance his header wide.
Claus Lundekvam made a crucial clearance after 36 minutes when Ameobi's cross looked destined for the unmarked Dyer who would surely have scored.
The woodwork came to Saints' rescue in the 42nd minute as Boumsong went close to breaking the deadlock with a header.
The visitors dominated the early stages of the second half and United were indebted to Shay Given and some wayward shooting.
First of all Robbie Elliott lost possession on the edge of the box to Jones who blasted over and Peter Madsen did exactly the same as the home defence was once again torn to shreds.
In between Jones could hardly believe it when Given pulled off a stunning save to prevent him from opening the scoring.
Everything good from United hinged around N'Zogbia and he set up the 68th minute winner. A powerful surge through the middle of the park saw him release Dyer who shot low and clinically to Bialkowski's left.
With their three substitutes already used, Saints had to play the last ten minutes with just ten players when Bialkowski fell awkwardly and was stretchered from the park with his left leg in a brace.
Dexter Blackstock - only on the pitch for four minutes - took over between the posts and was required to make only one save when he kept out substitute Albert Luque's quickly taken free-kick wide on the right.