Trailing 7-0 from the first leg, the home side went in front on the night when Alvaro Negredo rolled home.
And Neville was on course to celebrate a rare victory as Valencia coach before Barca substitute Wilfrid Kaptoum side-footed in a late equaliser.
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The result means Barcelona are unbeaten in 29 games, a Spanish record.
Their opponents in the final will be either Celta Vigo or Sevilla, the latter of whom lead 4-0 going into Thursday's second leg.
Neville is under pressure at Valencia, with the former Manchester United captain winless in nine league games since taking charge on 2 December.
He made it clear that Saturday's La Liga match with Espanyol was his priority by making sweeping changes, though Barca too named an under-strength team.
Lionel Messi, Luis Suarez and Neymar were all rested by Luis Enrique, who left 11 first-team regulars out of the squad.
The attendance at the 55,000-seater Mestalla was 16,200.
"I'm thankful for the fans who came to the stadium," said Neville. "Some didn't want to come and that was their right.
"We weren't playing under the best circumstances after what happened in the first leg last week, but the players played with dignity. We deserved to win.''
Barcelona reached the Copa del Rey final as they beat Gary Neville's Valencia 8-1 on aggregate after a 1-1 draw at the Mestalla Stadium.