Quique Sánchez Flores' side struck on the counter shortly before the half-hour mark, Antonio Blanco switching play to Ángel Pérez, who squared for Boyé to tap home.
It proved the only goal, with Alavés surviving a grandstand finish - including a passage of play that saw the ball come back off three separate posts - to seal a third straight unbeaten start and climb to the summit of the table.
Sánchez Flores was delighted with his side's intensity against a Villarreal team he rates highly.
"From the first moment it was a very intense match. We beat a really good side with extraordinary individual quality - it's very difficult to take the ball off them. We were very intense, and wherever the ball was, we had a lot of legs there," he said.
"It's fantastic and wonderful. It's a historic start after a long time. That means the fans, who we play for, have got something they haven't felt in years."
He also praised his midfield options: "The vast majority of matches are decided by what happens in the engine room, and we're very good there. Today it was Protesoni, Denis, Antonio, Mikel and Pablo who played."
Sánchez Flores praised Boyé's battling display, despite the striker being taken off with an adductor issue managed carefully through the game.
"Lucas was sensational. He's been carrying a groin injury and we've had to manage his minutes carefully. Today he had to play more than planned, but he plays very difficult games because he takes a lot of fouls," the coach said.
For Villarreal boss Iñigo Pérez, still waiting for his first win in charge, it was a painful defeat.
"Any defeat is painful. We were on an upward curve, with ideas that were starting to take hold. Today, for periods, we were getting there - we created chances and didn't take them. But the focus shouldn't be on what's settling in, it should be on what's costing us," he said.
He pointed to a tendency to switch off defensively when his new ideas are working well in possession: "When things are going well, you can fall in love with it, and when you need to snap into defending, there's a bit of lethargy. It happened to us in Santander, the Metropolitano was a different game. We need to defend certain situations better."
Pérez used a moment when the ball struck the woodwork three times in quick succession as a metaphor for his side's start to the season.
"I hadn't seen a triple post before. I thought it was going in. It's a good example of what's happening to us. We deserve it, we're playing well, and the attitude is good," he said. "The process is going well, I'm happy with the work, just not with the points we have," he added, insisting he never fears for his job and that his responsibility to the club runs deeper than any concern about results.