Lundstram, who has spent the majority of his career on loan spells in England's lower leagues, blasted into an unguarded net after Palace goalkeeper Vicente Guaita could only parry a low cross into the box two minutes into the second-half.
Despite the slender margin of victory, Chris Wilder's men were well worthy of the three points as they built on a promising 1-1 draw at Bournemouth on the opening weekend of the season.
Palace were blunt in attack with Wilfried Zaha often outnumbered and they have yet to find the net this season.
David McGoldrick missed a glorious chance to put the hosts in front before half-time, but his prodded finish from point-blank range was too close to Spaniard Guaita.
However, the Blades quickly made their mark after the break when a purposeful run and cross by Luke Freeman fell perfectly for Lundstram to fire home.