Wednesday had the better of the first half but Burnley bossed the second period and had the chances to pick up their first away win for five months.
Brian Jensen produced an eye-catching save to deny Wednesday a first-half lead as the Yorkshire side came close to breaking the deadlock after 30 minutes.
In-form striker Deon Burton - scorer in Wednesday's last three games – dithered in the area but recovered and slipped a neat pass to strike partner Marcus Tudgay.
Tudgay, scorer of two goals in last week's win at Wolves, worked his way into space and lashed a superb angled drive that almost beat the keeper but Jensen dived superbly to turn it away one handed.
Burnley were looking to improve their dismal record away from Turf Moor which has seen them go without an away win since November 5th.
And they might have shocked Hillsborough with an opener after two minutes but Michael Ricketts, on loan from Leeds, headed Alan Mahon's free-kick wide.
Wednesday, unbeaten in their previous three, came close to an opener when Burnley flapped at a long throw in from John Hills but Chris Brunt's header looped over the top.
After the break Burnley blew their best chance of going ahead when Mahon's corner was met by Frank Sinclair but his header was too high.
And when Mahon produced another dangerous ball in the closing minutes, Chris McCann's header was wide of the target.