Valencia, who lifted the trophy on their last appearance in the showpiece match in 2008, will meet 30-times winners Barca in the final on May 25 at Betis' Benito Villamarin stadium.
Marcelino's side fought back from two goals down to snatch a 2-2 draw in the first leg and a goalless home draw would have seen them through on away goals. They appeared to be set up to absorb pressure, inviting Betis to have most of the possession.
The visitors had the better of the chances in a tight and tense first period and it took a strong hand from Valencia keeper Jaume Domenech to turn over a shot from Jese, while Betis defender Aissa Mandi headed narrowly wide following a corner.
Valencia showed more ambition after the interval and went ahead with a well worked move in the 56th minute which saw Kevin Gameiro race into the box and slide the ball across for Moreno to comfortably tuck it into the empty net from close range.
That meant Betis needed at least two goals to progress and, while they continued to monopolise the ball, Valencia controlled the space and rarely looked like letting their lead slip.
Valencia coach Marcelino has reached a major final at last after losing three Copa semi-finals and one Europa League semi while in charge of Racing Santander, Villarreal and Valencia.
He said it was reward for a difficult season for his side, who are ninth in La Liga after drawing 15 of their 25 games.
"This is dedicated to our extraordinary squad which has suffered so much and deserved this prize," Marcelino told reporters.
"We have had some tough times, a lot of draws and a few defeats but we have always been a competitive team.
"The players deserve this and so do the club and fans after 11 years (since Valencia's last Copa showpiece). This coaching staff also deserves this and we're going to enjoy this final."
Barcelona, who have won the last four editions of the competition, beat Real Madrid 3-0 away on Wednesday for a 4-1 aggregate victory in the other semi-final.
Barca knocked Valencia out of the Cup at the semi-final stage last season and in 2016. The two sides have not met in the final since 1971, when Barcelona won 4-3 after extra time.
Valencia have won the competition seven times.
(Reporting by Richard Martin; Editing by Ken Ferris)
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