The last-gasp victory, which prompted wild celebrations at Celta's Balaidos stadium and sowed disbelief among the stunned Zaragoza players and coaching staff, left both sides still mired in the relegation places.
Both have 27 points with six games left, one less than 18th-placed Real Mallorca, with Celta in 19th and Zaragoza in 20th and last place due to an inferior head-to-head record.
Cristian Sapunaru nodded Zaragoza ahead in the 26th minute before Alex Lopez steered a header into the net off the underside of the crossbar eight minutes before the break.
Celta were on top in the frantic final stages and Bermejo clipped a Fabian Orellana cross into the net in the 92nd minute to secure what may prove a crucial three points.
"It was a very important goal in terms of our fight to stay in the first division," Bermejo told Spanish television broadcaster Cuatro.
"We got into difficulties early on in the match and the fact we managed to battle back is crucial," he added.
Celta were promoted at the end of last season after five terms in the second division, while Zaragoza have flirted with relegation the past three campaigns after returning to the top division in 2008-09.
Álex López was on the pitch for 60 minutes against.
He scored in the 36th minute and took five shots on goal.