The hosts had initially led through Jean-Philippe Mateta's early goal and were dominant for the entirety of the afternoon, while wasting numerous chances to put the game to bed.
Luton would go on to punish Palace, as Woodrow met Andros Townsend's cross in the final minute of additional time to clinch an unlikely draw.
Rob Edwards's side hardly laid a glove on the Eagles, but Oliver Glasner's side were unable to hold on for what would have been a second consecutive home win since taking charge for the Austrian.
The result moves Luton to within three points of safety, while Palace miss the opportunity to go an almost-unassailable 11 points clear of the drop.
In an unassuming opening 10 minutes, neither side really looked like threading the needle for an opener, but an error from the Luton defence allowed Palace in to take an early lead.
Alfie Doughty's slack back pass saw Daniel Munoz pounce in an advance position, and after rounding goalkeeper Thomas Kaminski, he was able to find Mateta, whose audacious flick caught everybody out, putting the Eagles ahead.
In a first-half devoid of much quality, it was another Luton error towards the end of the opening period that almost presented the hosts with a second goal.
Jordan Clark's carelessness to pass back to his goalkeeper inadvertently played Mateta through, but unlike Munoz, he could not successfully round Kaminski, and his effort from a tight angle only found the side netting.
The second period did not provide any more enthusiasm for the visitors, as Palace remained in control in terms of territorial domination, as both managers left it late to make personnel changes.
Mateta again had a golden opportunity to put the game beyond Luton, as he met Tyrick Mitchell's cross from point-blank range, but Kaminski was on hand to deny the Frenchman smartly with his feet.
Eberechi Eze was tidy in midfield all afternoon, but there was still time for him to showcase his flair, as the England international spotted Kaminski off his line, and from the halfway line, he was just inches from finding the net, as his effort skimmed the crossbar on the way over.
Despite needing a goal, Luton continued to face wave after wave of Palace pressure, as Issa Kabore needed to make a last-ditch challenge to deny Mitchell right at the end of the 90.
Six minutes of stoppage time provided no respite for the Hatters either, as substitute Odsonne Edouard struck the crossbar from the edge of the area when given the freedom of Selhurst Park to unleash an effort at goal.
Nobody inside Selhurst could have predicted what was to come next though, as Luton's only real attack of note in the second half resulted in their equaliser, as Woodrow's flick on from Townsend's delivery evaded everyone and nestled in the bottom corner.
The Palace support were visibly furious for not putting the game to bed, while there was delirium in the away end, as that point could prove vital in the latter stages of the campaign for the Hatters.
This result also means Luton have avoided losing five straight league games for the first time since 2019, and puts them in good stead ahead of their trip to Bournemouth in midweek.