Serbia midfielder Milivojevic celebrated his 100th appearance for Palace when he netted a 21st-minute penalty and Townsend sealed the win with a neat stoppage-time goal after he was put through by the lively Wilfried Zaha.
Palace dominated early on as Zaha curled a shot narrowly wide in the first minute and Jordan Ayew drew a good save from visiting keeper Ralf Fahrmann, who limped off injured midway through the first half after making his debut for Norwich.
Todd Cantwell then missed a sitter for Palace while Finalnd striker Teemu Pukki twice came close for the visitors who pressed hard in the second half but failed to create much up front against a packed and well-organised home side.
With time running our for promoted Norwich, Zaha broke down the left flank and gave Townsend the simple task of turning the ball past reserve goalkeeper Michael McGovern into the bottom corner of the net.
Palace, ninth on 11 points from seven games, equalled a club record of six successive unbeaten league matches at home while Norwich, hovering just above the relegation zone with six points, stretched their winless away league record to 16 games.