Loren Moron put Betis ahead on the stroke of half-time and Valencia were left with a tall task when goalkeeper Jaume Domenech allowed veteran winger Joaquin to score direct from a corner.
Head coach Marcelino responded by sending on Gameiro and the French striker crossed for Denis Cheryshev to head Los Che back into the tie.
Then, in stoppage time, Gameiro slid in a second – and potentially crucial – away goal from Rodrigo Moreno's cutback.
The Betis defence was still readjusting to the early departure of Marc Bartra through injury when Junior Firpo bundled Rodrigo to the floor and Dani Perejo's free-kick was deflected behind.
Despite their hosts' industry, Valencia were creating the clearer openings and Joel Robles produced a stunning reaction save when Rodrigo steered Carlos Soler's pass towards goal.
Santi Mina headed the resulting corner against the top of the crossbar but Betis almost led in the 34th minute as Andres Guardado's angled volley from Sergio Canales' cross bounced agonisingly wide.
Canales delivered again in first-half stoppage time, with Sidnei heading back across goal for Loren to nod in.
Bartra's replacement Javi Garcia almost put through his own goal early in the second half but a more glaring lapse saw Betis double their advantage.
William Carvalho lashed wastefully over from a scramble at a 54th-minute corner – an event that became academic when replays showed Domenech had pushed Joaquin's in-swinger away from behind his goalline.
That meant it was time for Gameiro, still sporting a nasty black eye from his weekend collision with Gerard Pique, to enter the fray and he chipped to the near post in the 70th minute for Cheryshev to find a stooping finish.
The same combination resulted in Cheryshev heading against the bar a minute from time and Gameiro's late equaliser made sure Quique Setien's wobbling side would not hold on to a first-leg advantage.
What does it mean? Late show gives Valencia the edge
Like Wednesday's Clasico at Camp Nou, which was played out on a knife edge to a 1-1 draw, Thursday's Copa semi also ended all square. Somehow, this does not feel as delicately poised and the Betis players on their haunches at full-time told a story: this is a team that feels they blew their chance.
Gameiro the catalyst on his return to Seville
As a former Sevilla favourite, Valencia's saviour will have enjoyed this salvage job against their bitter rivals that little bit more. He gave the visiting attack a focal point it had lacked and his intelligent movement was too much for the Betis back three to contain.
Domenech clanger could prove decisive
In line with the modern trend of clubs playing their back-up goalkeeper in cup competitions, Domenech has been an ever-present on the way to the semi-finals. His wretched misjudgement on Joaquin's goal could still prove costly despite Gameiro's heroics.