Newcastle led 8-0 at half time. Hall Charlton's break from the ruck set up Stuart Grimes for a try.
Almost on half time Walder kicked a penalty and then added a second after the break when Epi Taione blasted down the right wing.
The England cap then slotted a superb drop goal but missed three kickable penalties as Newcastle stepped up the pace.
They were worrying misses but the Falcons were in the driving seat and they should have made a lot more of another snappy Charlton break but the support was too slow in arriving.
Leeds had Gavin Kerr sin-binned for preventing the ball being released at a ruck, but they could still have cut three points off the lead when Dan Parks tried a snap drop goal that flew wide.
Inga Tuigamala and Taione combined to set up good ball and Tom May linked with Walder to send in Mike Stephenson for a 69th minute try.
Eddie Jones crashed over from a line-out drive near the end to make it 19-8, but it was too little to late.
