Neil Warnock's side have now failed to win any of their last four matches, but at least produced an improved performance on the midweek home defeat to Nottingham Forest.
Since winning the Steel City derby only a fortnight ago, Wednesday had lost three successive Championship matches and, despite returning to South Yorkshire with a hard-earned point, look set for a relegation battle this season.
In a humdrum encounter, the Owls took a seventh-minute lead when Leon Clarke turned Lewis Buxton's cross past Julian Speroni in the Eagles goal.
When Palace tried to hit back, Craig Beattie's 25-yard free-kick flew over the bar and, just before half-time, Lee Grant saved John Oster's drive and tipped Paul Ifill's extravagant scissor kick away for a corner.
Warnock's side improved after the break and deserved their 54th-minute equaliser when Shefki Kuqi was upended inside the area and Ben Watson coolly sent Grant the wrong way from the penalty spot.
The Owls almost restored their lead three minutes later though when Paddy McCarthy's error allowed Leon Clarke to fire a left-footed shot narrowly wide.
Palace also had their chances to win the match and, when Oster's dangerous cross eventually found its way to Kuqi, the former Finland international's first-time effort flew over the bar.
Wednesday almost secured only their second away victory of the campaign when Jermaine Johnson crashed a shot against the top of the bar while at the other end, with only three minutes left, substitute Sean Scannell was denied by Grant.