The runaway La Liga leaders were 18 minutes from a first top-flight defeat of the campaign after John Guidetti gave the struggling visitors a shock first-half lead at Camp Nou.
But goals from Luis Suarez and Lionel Messi turned the game on its head and secured a 2-1 win for Barca, restoring their 11-point advantage at the summit.
An impish dribble and delicate cross from Iniesta made the Uruguayan striker's goal possible and Valverde was keen to pay tribute to the 33-year-old Spain great afterwards
"The truth is that we have good players who play in the interior role, but Iniesta is a master at that," said Barca's coach after guiding his side to a record-equalling 21-game unbeaten start to the top-flight campaign.
"I thought he could help us from there. It was important not to get too many of us in the Alaves box. It would have provoked counter-attacks.
"For that we needed players who move well in space like Leo and him. It was an extraordinary move and the goal let us breathe."
Alaves saw late penalty appeals against Barcelona centre-back Samuel Umtiti rejected and protested to the officials after full-time, although Valverde was quick to dismiss their complaints.
"Apart from cutting off his hand, we couldn't do anything," he said, having seen Messi's stunning free-kick seal maximum points six minutes from time. "I think it's involuntary, but each one can see it from their point of view.
"Sometimes the ball goes in and they don't give it, other times this can happen.
"They complained a lot about it. Umtiti told me it was not deliberate.
"There are always controversies – sometimes they hurt you and sometimes they help you."
Philippe Coutinho began brightly on his full Barcelona debut, but was substituted after the hour as Valverde introduced striker Paco Alcacer to chase the game.
"They [players] are not machines who can just go into a new factory and start to work immediately, but I saw him doing well, involved in the play, wanting the ball," said Valverde when asked about the Brazil playmaker's performance.
"It's another step. The other day he played 20 minutes and now a bit more. We will see him go in bit by bit."