Three penalties from the boot of Jimmy Gopperth (pictured) and a close-range try from hooker Rob Vickers gave the Falcons their second successive Premiership win as Worcester toiled to match Carl Hayman and the Newcastle pack who were in control throughout.
Both sides found the swirling wind and soaking wet pitch a problem in the opening minutes.
But Newcastle hammered the Worcester pack at three successive scrums and a rolling maul and the Warriors were grateful to escape at a wheeled scrum under their own posts, Willie Walker getting the ball into touch.
The Falcons kept up the pressure at successive five-metre scrums and, when Mark Sorenson was pulled down just short from Micky Young's inside pass, hooker Rob Vickers picked up to be driven over for the opening try in the 15th minute.
Newcastle wasted two good chances and little was seen of Worcester in attack apart from a line-out driving maul which the Falcons turned over and cleared before Gopperth kicked a 28th-minute penalty to make it 8-0.
Gopperth added a second penalty nine minutes into the second half when Worcester strayed offside but the Warriors saw more the ball after the break and Willie Walker kicked a much-needed penalty to get them back in the game at 11-3 in the 61st minute.
Newcastle upped the pressure in the last 10 minutes but it was real error-strewn stop-start rugby with Gopperth slotting his third penalty in the 75th minute to put the Falcons out of reach.