They were denied in the early stages by some excellent work by the Crewe keeper Steve Collis, who saved well in the opening minutes from both Paul Hayes and Matthew Sparrow.
But United finally went in front in the 38th minute when Gary Hooper did well to square the ball back from the right by-line to provide a simple finish for winger Martyn Woolford.
Crewe, with only one point from five games on their travels this season, were unlucky not to be back on level terms just before the interval, when a flashing header from striker Tom Pope was brilliantly turned away by goalkeeper Joe Murphy.
It was in the second that Scunthorpe worked up a full head of steam, rattling the woodwork twice as Crewe struggled to survive.
First Hooper cut in from the left to fire a right-foot shot against the outside of the near post.
Then Woolford surged forward to rattle the underneath of the crossbar with a shot from the edge of the box.
But Scunthorpe were not to be denied and made it 2-0 in the 67th minute when Hooper once again was the provider with a deft touch to Paul Hayes, who finished well past goalkeeper Collis with a fierce shot from level with the penalty spot.
Hayes had the ball in the net again just four minutes later but his header was ruled out for offside.
The third goal that Scunthorpe needed to take them top of the table on goal difference came in the 80th minute when skipper Izzy Iriekpen rose high at the far post to head home a corner from Woolford for his third goal in successive games.
Scunthorpe finished strongly without being able to add further to their score, but for Crewe it was another disappointing afternoon in a game in which they had started brightly.
Defensive mistakes proved their undoing, leaving the Railwaymen deep in trouble near the foot of the table.