The result always seemed safe, though, as Madrid progressed through a 29th consecutive Champions League group stage, with Gladbach also advancing after Inter and Shakhtar Donetsk drew 0-0.
Failure to go through could well have seen Zidane's position become untenable, and the Madrid boss was delighted with the way his side performed under pressure.
"This was the objective: to finish first," he said, as quoted by Marca. "We played a spectacular game, from the first minute to the last. We interpreted the game really well.
"I think this was the most complete game of the season. I've been a player and it's impossible to play like this all the time. We try to, but every now and then...
"We don't only perform under pressure; we have played other good games as well. It's true this team has that [quality]: when the difficulties are great, it appears.
"I'm happy for the players because they are the most important thing. I'm fighting with them and I'm happy for them. It was a good game."
Benzema's pair of headers means he has been involved in 11 goals in all competitions this season, the joint-most of any LaLiga player.
The striker's double took his tally to 51 goals in the group stages, a figure bettered only by Raul (53), Cristiano Ronaldo (67) and Lionel Messi (71).
"It was a difficult game," Benzema said. "We started well, we were eager to win and to show we're the best and that we were going to work together to win this game.
"When we give everything on the pitch, we get goals and we could have got more. If we always play like today..."