The 31-year-old stole the show to pile on the agony for the struggling Yorkshire side, who have now got off to the worst start in their 140-year history and not scored a league goal for more than five hours.
Blake plundered his first league goal since his £250,000 return to Burnley for his second spell at the club, and grafted to create the second finished off by Chris McCann.
Wednesday - still backed by crowd of 18,359 - came within a whisker of a dream start.
But keeper Gabor Kiraly produced a super block as Wednesday threatened to break their desperate goal drought after 14 minutes.
Francis Jeffers and Akpo Sodje's crisp one-two saw Sodje produce a super pass for his strike partner. Jeffers switched feet and smashed his angled shot from 12 yards but Kiraly beat it away.
It triggered a quick break that stunned the home side. Wade Elliott's cross from the right was half-cleared and Blake wrong-footed the home defence, switching the ball to his left foot and lashing in a low drive from 15 yards to beat Lee Grant.
A wild mis-hit shot from Etienne Esajas almost gifted Wednesday a chance when he misdirected his effort across the face of goal, but Wade Small was inches short turning it in.
Ten minutes before the break Kyle Lafferty was first onto a loose ball just inside the area, but Wednesday survived when his shot smacked into Richard Wood.
As the dejected home side trooped off at the break they had reached another unwelcome milestone - five hours of league football without a goal.
And two minutes into the second half Wednesday's misery deepened. Blake chased Frank Simek and robbed the defender before cutting back and inviting ball for McCann who rifled in an angled shot.
Under pressure Wednesday manager Brian Laws wielded the axe after 59 minutes by bringing off strikers Sodje and Jeffers for Marcus Tudgay and Deon Burton.
But it was Kenny Lunt who came closest with a blistering free-kick from 25 yards that was tipped around the post by Kiraly.