The former England striker started his first match in 14 months at the ground where he scored on his Liverpool debut as a 17-year-old against Wimbledon in 1997.
But 16 years on Owen, reprising his England strike pairing with Peter Crouch, lasted just 53 minutes without managing an effort at goal.
The duo were playing together for the first time since both came on as half-time substitutes in a 1-0 defeat by France in 2008.
And the old partnership could have given Stoke the lead in the 12th minute when Owen got his head to a corner. The ball looped across goal but Crouch could only direct it wide from six yards out.
In the second minute Wilfried Zaha played in Jermaine Easter with a diagonal pass and the striker's curler from the right-hand corner of the area was tipped away by Thomas Sorensen.
Five minutes before half-time Zaha pounced on Robert Huth's mistake on halfway and raced into the box, chased manfully by the Stoke centre-half, but his angled drive was turned away by Sorensen.
Yannick Bolasie remained a threat for Palace, teeing up Andre Moritz for a shot which the Brazilian mis-kicked horribly before forcing Sorensen into a diving save from 20 yards.
Palace sub Jason Banton hit the side-netting while, for Stoke, Charlie Adam's ambitious lob flew wide.
But neither side could find a winner and, although Palace were the better side, the promotion chasers face a replay they could probably do without.