It doubled the tally for the season for the 37-year-old forward who had netted only twice in his previous 16 starts.
And it helped in-form Scunthorpe stretch their unbeaten run to five games under the charge of caretaker boss Russ Wilcox.
Burton opened the scoring in the 17th minute, tapping home at the far post after a low right-wing cross from Christian Ribeiro.
He struck again in the 33rd minute, controlling the ball on the edge of the box and turning to drill a left-footed shot low into the bottom left-hand corner past goalkeeper Barry Roche.
Midfield men Marcus Williams and David Syers could have put the result beyond doubt before half time as Morecambe wobbled after a bright start which saw them force seven corners in the opening seven minutes of the game.
There was no way back in the second half for the visitors as Scunthorpe stood firmly in control before threatening to increase their lead again through Syers twice and then his midfield colleague Sean McAllister, who were both denied by keeper Roche.
And in the closing stages Burton was denied a hat-trick when his volley from a corner was cleared off the line by full-back Robbie Threlfall.