Blake, however, only had to wait a couple of minutes to make amends as James O'Connor got to the by-line and his cross was deflected as far as Blake, who fired home giving Joe Murphy no chance.
Blake then tried his luck when he was well found by Joey Gudjonsson, but this time drove wide from 20 yards.
Scunthorpe's top-scorer Martin Paterson had the Irons' first chance but although he managed to lob the ball over the advancing Brian Jensen his attempt drifted well wide.
Jensen then had to be alert on his near post to save a Grant McCann free-kick.
The same player showed he was not afraid to shoot from distance as he let fly from fully 25 yards with a shot that struck a post, with Jensen scrambling across his goal.
Scunthorpe's misfortune was compounded as Gudjonsson found Elliott with a crossfield pass. Elliott skipped to the by-line and beat Marcus Williams before picking out Akinbiyi to score with a close-range header.
With half-time approaching, Blake then drove a free-kick past Murphy but just wide of the target.
United boss Nigel Adkins made a double change at the break, replacing Ian Morris and Ben May with Jim Goodwin and Paul Hayes, but in truth the visitors rarely troubled Jensen.
At the other end, a right-wing cross from Graham Alexander was met firmly by the head of Chris McCann, but Murphy produced a super save to push the ball behind for a corner.
With ten minutes remaining, Blake went desperately close with a free-kick that saw Murphy stranded, but the ball whistled past the post.
The result was a third successive victory for Clarets boss Owen Coyle, whose side are now just a point away from the play-offs, while Scunthorpe remain rooted in deep relegation trouble.