Two first-half goals in 10 minutes from George Bowerman and Kayode Odejayi did the trick as the home team struggled badly to respond.
Accrington opened the scoring in the 26th minute when striker Bowerman cut inside from the right like a knife through butter to drill an excellent angled shot into the far corner of the net.
They almost struck again when midfield man Kal Naismith was allowed a free run to the edge of the box where he unleashed a fierce drive that whistled just wide.
They did make it 2-0 in the 36th minute when veteran striker Kayode Odejayi bustled in at the far post to head home a left-wing cross from Bowrman.
Scunthorpe, who were booed off by their own fans at the interval, offered nothing in reply apart from one header from leading marksman Sam Winnall that flashed just wide.
United brought on new loan signing Reuben Noble-Lazarus from Barnsley for his debut at the start of the second half as part of a double substitution.
He made an immediate impression, rattling a post with a rasping 25 yard effort as Scunthorpe tried to get back into the game.
But it was Accrington who almost struck again when Peter Murphy walked through a wide open home defence to force a good save from keeper Sam Slocombe.
The one real save of the game for Accrington keeper Marcus Bettinelli came midway through the second half when he reacted well to keep out a close-range header from Winnall.