The Glasgow side would probably have settled for a point ahead of this meeting with the Spanish League high-flyers before the United States international handed them a first-half lead.
But a dream night turned into a nightmare for Edu when he inadvertently headed into his own net just a minute into the second half to allow the visitors to return to Spain with a share of the points, before both teams meet again early next month.
Rangers handed Champions League debuts to Richard Foster and Vladimir Weiss, after Kirk Broadfoot failed a late fitness test on a foot injury.
Allan McGregor, who had so far kept a clean sheet in this competition, was back from his suspension at the weekend.
Rangers were forced to soak up some early pressure as Valencia dominated the opening stages.
The Spaniards could have claimed an early lead when Steven Whittaker gifted possession to Pablo Hernandez but his shot from distance was smothered by McGregor.
The home side had a chance of their own when Steven Davis picked out Kenny Miller with a 40-yard pass but goalkeeper Cesar Sanchez raced off his line to clear the danger before the lone striker could even unleash the shot.
Rangers gradually began to impose themselves on the game and should have been ahead when Miller turned provider for Steven Naismith but he was denied a repeat of his winner against Bursaspor when he fired straight into the hands of the goalkeeper in front of goal.
The roles were then reversed when Naismith delivered a great ball from the right flank for Miller only for the striker's header to be blocked at the near post by Sanchez.
The Scottish champions claimed for a penalty for a shove on Whittaker in the box but the pleas were ignored by referee Nicola Rizzoli, before Sasa Papac forced Sanchez into action again with an ambitious shot that was tipped just over the crossbar.
Rangers' impressive spell continued when Miller raced onto a Davis ball and bore down on goal only for Valencia's number one to be alert yet again and snuff out the threat before he could dispatch a clean shot into the back of the net.
At the other end, David Navarro threw himself in front of a Juan Mata cross only to see his header flash just past the post from six yards.
But the Scottish champions' pressure eventually paid off when they surged into the lead with 34 minutes gone. Weiss whipped an inviting corner into the box where Edu was waiting to rise above everyone else and send a firm header past Sanchez.
Walter Smith's men then spurned a great chance to double their advantage before half-time when Edu saw his shot crash off the post, with the rebound falling perfectly for Miller who somehow managed to blast over instead of leaving the net bulging.
Instead, Rangers suffered a devastating setback just a minute after the restart when Valencia were able to haul themselves back into the game after Edu nodded a Tino Costa free-kick into the back of his own net.
They could have restored their lead when Madjid Bougherra embarked on a powerful run, holding off the threat of a couple of opposition players, before slipping the ball into the path of Miller but Sanchez was first to the ball.
The goalkeeper then did well to produce a one-handed save to guide a Davis effort over, after the midfielder had tried to lob high into the net.
Naismith found the empty net at his mercy only to send his half-volley wide of target, failing to get enough purchase on the effort. Foster then lashed over after another Naismith shot was blocked.
McGregor came to the rescue of Rangers in injury time with a superb save to deny substitute Roberto Soldado as the tie ended level.
Although disappointed not to win the match, the performance would no doubt have acted as a confidence-booster ahead of this weekend's crunch Old Firm derby, with Rangers and Celtic heading into the clash locked on the same points at the top of the Scottish Premier League.