Louis Saha and Jermaine Beckford got the Merseysiders off to a flying start at Glanford Park before Seamus Coleman, Marouane Fellaini and Leighton Baines made sure of victory.
Scunthorpe were completely outplayed aside from a brief spell at the start of the second half when Michael Collins threatened to spark a comeback with a superb strike.
There was a large media presence at the match but Everton were in no mood to surrender to the potential upset that may have been anticipated.
Scunthorpe went into the game on the back of seven defeats in eight games and having lost their last six at home.
Defeat would have been a huge embarrassment for David Moyes and his side but he showed in his selection of a strong team that he had no intention of letting that happen.
Everton displayed no sign of nerves and took control early on.
Coleman went straight onto the attack and sent over a cross in the first minute which Joe Murphy had to push over the bar.
The visitors maintained the pressure and claimed the lead after just four minutes through the resurgent Saha.
The Frenchman, who scored his first Premier League goal in 11 months against Tottenham on Wednesday, found space on the edge of the box and hit a low left-foot shot past Murphy.
Former Scunthorpe striker Beckford had a chance to add a second when he broke through moments later but Rob Jones managed to get a foot in as he prepared to shoot.
Beckford was similarly denied another opportunity by Andrew Wright and Marouane Fellaini blazed over as the Toffees dictated the pace.
Scunthorpe did get an opening as Chris Dagnall headed wide and Martyn Woolford then shot straight at Tim Howard from distance.
They were rare opportunities and Beckford looked certain to add a second for Everton after being played through by Coleman but Murphy produced a fine save.
Leon Osman also had a glorious chance as Baines picked him out in front of goal but the midfielder's close-range effort was deflected wide.
It came as no surprise when Everton doubled their lead after 33 minutes.
Osman was the provider from out wide, the stand-in captain whipping in a cross for Beckford to glance in at the near post.
It was a sweet moment for the striker, who helped the Iron to the League One title during a loan spell four years ago.
Saha almost claimed a third on the stroke of half-time as Murphy tipped over a firm header from a Baines cross.
It seemed a case of how many Everton could score but the Iron returned for the second period a side transformed.
Within seconds of the restart the underdogs had pulled themselves back into the game with a stunning goal from Collins.
The midfielder outpaced Sylvain Distin as he raced onto a long ball from Josh Collins and unleashed a ferocious strike from the edge of the area which flew past Howard.
Everton were caught cold and Scunthorpe poured forward in search of another opening.
Dagnall fired wide from distance and Distin cut out a dangerous cross from Eddie Nolan with a firm header.
Yet just as the hosts were threatening one of the great cup fightbacks, Everton snuffed out the revival with a third goal.
Beckford beat Wright on the left and sent over a cross for Coleman to powerfully head home his fifth of the season.
That appeared to take the sting out of the contest and Coleman volleyed over as Everton reasserted their superiority.
Fellaini made certain of Everton's presence in the fourth round with the fourth goal after 73 minutes.
The Belgian was given time on the edge of the box and took a couple of touches before firing a left-foot shot across goal and beyond the reach of Murphy.
Baines put the gloss on the victory late on as he eased past tiring defenders and clipped a fine shot into the top corner from the corner of the area.
David Mirfin went close to a Scunthorpe consolation after neat turn and shot from the edge of the box which Howard tipped over.
Michael Raynes also had a header blocked on the line by Howard in the hosts' final flurry.