The Owls went down 4-1 at Ipswich Town in last August's opener, losing six in a row to leave them battling relegation until May.
Wednesday snatched the lead in dramatic fashion after just 30 seconds, centre-back Mark Beevers picking out Akpo Sodje on the left flank, his pass inside fell nicely for Marcus Tudgay, who picked his spot from 15 yards, the ball looping over Diego Penny.
The Sheffield side were two up on four minutes, Deon Burton threading the ball to Sodje, who drilled his right-foot strike into the roof of the net past the astonished Penny.
Burnley hit back two minutes later as Wednesday relaxed, Wade Elliott's precise cross finished off from close range by Martin Paterson, making his debut for the Lancashire side after moving from Scunthorpe in a £ 1million deal.
Burton twice went close heading over the top from eight yards before Wednesday hit the target again on 16 minutes. Jermaine Johnson was the architect twisting past his marker before sliding the ball to Sodje, lurking at the far post, who sidefooted past Penny.
Goalscorer Sodje's game came to a premature end six minutes later, the big striker limping off to be replaced by Leon Clarke.
Lee Grant pulled off an eye-catching stop three minutes after restart tipping Chris McCann's stinging long-range strike round the post at Burnley looked for a way back.
Full-back Tommy Spurr almost found a way through before Tudgay finished off Burnley, Clarke squaring the ball to the midfielder, who beat Penny from 12 yards.
Wednesday could have had more, the Burnley keeper pulling off stunning saves to keep out both Clarke and Tudgay.