Some shaky play in back led to Celta take a surprise early lead through Santi Mina in the fourth minute, but Benzema hit back for the hosts 20 minutes later after some nice interplay from Real Madrid.
The Frenchman was unplayable at times as Madrid were reunited with their fans for the first time since March 1, 2020.
They played the whole of last season at reserve team Castilla's Alfredo Di Stefano ground at their training complex.
"I feel good, I've got the support of the coach, the president, the players and the crowd," Benzema said.
"It's a special night for us with the fans here and the atmosphere. It was a little strange to be playing in front of fans again, but they got right behind us. We need their support and they gave us everything today."
The joy at the Santiago Bernabeu was short-lived, though, as Franco Cervi knocked the rebound from his own clever shot into an empty net after Thibaut Courtois was pulled off his line trying to help stop a quick-hitting counter-attack from Celta, who took a 2-1 lead into half-time.
Benzema scored straight out of the gates after the break with a lovely header back across the goal from Miguel Guttierrez's outswinging cross to get Madrid back on level terms for the second time in the game.
Vinicius Junior then fired Real ahead before the hour mark with Benzema now the provider, the Brazilian latching on to a through ball and calmly slotting home after a good run and new arrival Eduardo Camavinga doubled the lead for Carlo Ancelotti's side from a rebound to open his account in LaLiga.
"A really good night, almost everything went well. It wasn't perfect, but above all the fans helped us a lot," Ancelotti said after the match. "We lost the ball twice, and we have to work on that. In attack we were exceptional.
"Of course we have to improve [the mistakes], it make the game complicated for us. The reaction allowed us to win, but we mustn't give those balls away. We need more balance. We'll talk about what we didn't do well."
Benzema put the three points in the bag to complete his hat trick from the penalty spot after Denis Suarez fouled Vinicius in the area shortly before half-time.
Real had started the process of reforming their stadium just before the COVID-19 pandemic struck, modernising the ground and adding a retractable roof.