The Clarets comfortably secured their third win on the bounce to put themselves firmly back in the play-off picture.
First half goals from Robbie Blake and Ade Akinbiyi were enough to secure a 2-0 win for Owen Coyle's side, who moved to within one point off a place in the top six, albeit until mid-week when the rest of the Championship play.
A well-worked corner on six minutes found Blake, who evaded a couple of challenges and perhaps should have opened the scoring, but fired over the bar from six yards.
However, the Clarets talisman made amends three minutes later when his superb right-footed shot from the edge of the box curled past Joe Murphy and nestled into the bottom corner for his third goal in as many games.
The Burnley defence had to be alert on 12 minutes when a ball over the top found Martin Paterson racing down on goal.
He flicked the ball over the on-rushing Brian Jensen, but thankfully a hopeful lob was wayward and Graham Alexander was able to see it out for a goal kick.
Scunthorpe were then just a whisker away from dragging themselves level when a speculative effort from 45 yards from Jack Cork, with Jensen scrambling, crashed against the post before rebounding to safety.
But the lead was doubled on 32 minutes when a superb cross by Wade Elliot, after excellent play from Blake and Gudjonsson was headed home from close range by Akinbiyi.
The Clarets played some excellent football, particularly in the opening 45 minutes - and a Blake free kick right on the stroke of half time could have added to the visitors' misery but it flew just wide of Murphy's right-hand post.
That was the last real chance of the half and the Turf Moor faithful were delighted to go in at the break 2-0 up.
It was a quieter start to the second half Scunthorpe looked to reduce the deficit.
The introduction of Goodwin and Hayes at the break for the visitors gave them a much-needed lift but even the fresh legs couldn't trouble the Clarets, who comfortably kept Scunthorpe at arms-length.
Blake was put free by Elliott on 63 minutes, but the former Bradford striker was well challenged and had to settle for a corner which unfortunately came to nothing.
More one-touch football almost led to a third from the Clarets on 69 minutes, but this time Elliott cold only divert a magnificent Jon Harley cross wide under pressure in the six yard box.
Burnley were starting to get back in the groove though and a Chris McCann header was well saved by Joe Murphy from point blank range.
A free kick from Blake on 81 minutes then curled inches wide with Murphy struggling to get across his goal, as the Clarets looked to put the game out of sight of Scunthorpe, who struggled all afternoon to get a foothold in the match.
In the end, the second half may not have been as free-flowing and attacking as the first 45 minutes, but never mind the quality - feel the league position as Burnley fully deserved their win at a freezing cold and blustery Turf Moor.
Burnley: Jensen, Alexander, Varga, Unsworth, Harley, Elliott, Gudjonsson (Spicer 76), McCann, J O'Connor, Blake (G O'Connor 88), Akinbiyi (Caldwell 90).
Subs: Kiraly, Caldwell, Jordan.
Booked: Harley (foul, 61)
Scunthorpe United: Murphy, Butler, Hobbs, Martis, Williams, Sparrow, Cork, McCann, Paterson (Forte 64), Morris (Goodwin, 45) May (Hayes, 45).
Subs: Lillis, Hurst.
Booked: Williams (unsporting behaviour, 29), Sparrow (foul, 51)
