Both sets of fans held a minute's applause on 11 minutes in memory of former Leeds and Newcastle midfielder Gary Speed, who died just under five years ago.
Leeds have been much improved since the appointment of former Swansea manager Garry Monk as manager, but were incapable of stopping a talented Newcastle side.
While Newcastle deserved the win, the Magpies' first goal could have been easily prevented. Jack Colback's long range effort should have been comfortably saved by Rob Green, but the former England 'keeper comically spilled the shot, allowing Gayle to tap in from close range.
Newcastle and Gayle got their second when Vernon Anita and Ayoze Perez linked up down the right, with Anita squaring for Gayle who made no mistake once again with the finish.
Newcastle saw out any threat that Leeds posed and Rafa Benitez's men went five points ahead of second-placed Brighton and nine points of Reading who sit in third, just outside the automatic promotion places.
Meanwhile, Leeds' three-match winning streak came to an end and sit just outside the play-off places, one point of sixth-placed Norwich City.