It was hardly a classic but the majority of the 8,864 crowd went home happy as Newcastle extended their unbeaten Premiership run to three games.
James Brown missed a relatively easy early penalty before Burke belted over one from over 55 metres to give Newcastle the lead in a lively opening 10 minutes, but the Falcons gave away a string of penalties at the line-out.
Twice the Falcons pack destroyed Worcester´s scrum and referee Ashley Rowden´s decision to penalise Newcastle when the scrum went down was rightly treated with derision by the crowd, as was his inability to see Worcester players on the wrong side of the ball as Newcastle launched a wave of attacks.
Two real scoring chances were squandered when Burke´s pass to Mathew Tait gave the winger little chance of taking the ball and then Walder´s crossfield kick was just out of the reach of the chasing Joe Shaw.
Newcastle´s line-out transgressions caught up with them when Owen Finegan was sin-binned for pushing but the Falcons destroyed the Worcester rolling maul from the line-out penalty and forced the Warriors to run it.
When Mike Maguire lost the ball, Burke hacked it 70 yards down field and was there again when Thinus Delport could not gather and he snapped it up to dive over and then converted from wide out.
Newcastle were caught stretched wide out when Thomas Lombard kicked through and `Aisea Havili scrambled between Burke and Tait to touch down for a try which Brown converted from the touchline, but Burke made amends with his second penalty just before half-time.
Newcastle lost two of their own line-outs early in the second half and conceded a penalty which Brown kicked to make it 13-10.
But Worcester again lost the ball when it looked like they must score and Walder snapped it up when Jonny Hylton could not hang on.
Walder raced 80 metres, shaking off tackles by Hylton, Delport and Simon Whatling to score.
He was hurt in the process and replaced by Toby Flood.
Burke missed the conversion but kicked a penalty when Tony Windo went over the ball right in front of the posts but the Worcester captain made amends when he was driven over for a try from a line-out, although the Falcons players were adamant he had not touched down.