The well-travelled midfielder's goal not only earned his side a point but also prevented Los Che from moving above Malaga into fourth place.
Instead they must settle for a share of fifth and will surely rue switching off after Jonas and Roberto Soldado had turned around Vicente Iborra's opener for Levante, who remained in mid-table.
The big talking point before the game kicked off was the news that Levante top scorer Obafemi Martins had been left out of the starting line-up after revealing to the media that he wanted to leave the club to join Major League Soccer side the Seattle Sounders.
However, even despite the absence of the Nigerian striker, Levante struck first.
Juanfran delivered a corner which was flicked on by the head of Iborra over the poorly positioned Valencia goalkeeper Vicente Guaita and into the net.
Before the goal, the only incident of note had been when Valencia full-back Jaoa Perreira clattered into referee Carlos Velasco Carballo, and the game was delayed while the official recovered from the clash, but he was eventually able to continue.
Both sides were grateful to their goalkeepers for preventing further goals before Valencia got back on level terms, with Jonas eventually scrambling the ball home after Levante failed to clear the danger and Canales could not convert from yards out, so the Brazilian did instead.
Ernesto Valverde's side then took the lead deep in injury time of the first half thanks to a Soldado special. Sofiane Feghouli put in a cross which fell awkwardly for the Spain international, but Soldado swivelled to strike the ball first time on the volley and in off the crossbar.
Soldado had a frustrating second half. First he had a goal chalked off for offside and then he hammered a shot against the bar, one of several chances the hosts would regret not taking when Barkero equalised with a minute remaining.
The midfielder ran on to a throw-in but could not control the ball, but slow reactions from David Albelda and a slip from Jeremy Mathieu gave him an opportunity which he did not waste, smashing the ball into the bottom corner.
Valencia could have snatched a winner in injury time when Dani Parejo's free-kick was pushed out by Gustavo Munua into the path of Feghouli, but the Algerian blazed over from close range.
Valencia remained fifth in the La Liga table, level on points with Malaga, who host Atletico Madrid on Sunday, while Valencia stayed in 10th.