Los Blancos, back in action for the first time since the European Super League project crumbled, broke the deadlock after 30 minutes through Benzema's penalty, which was given on VAR review.
Alvaro Odriozola swiftly headed in a second, with Benzema adding another shortly before half-time as Real took control.
Zinedine Zidane's men, who had earlier confirmed midfielder Federico Valverde had tested positive for Covid-19, enjoyed most of the early possession, and took the lead on the half-hour.
Vinicius went down in the penalty area, but the referee waved away protests before going over to view the incident on the pitchside monitor and then deciding there had been a trip by Isaac Carcelen.
Benzema slotted the spot-kick past Jeremias Ledesma to register a 20th LaLiga goal of the campaign.
Before the home side could regroup, they fell further behind in the 33rd minute.
This time Benzema turned provider, crossing from the left for Odriozola to head in at the far post.
The France striker then scored a second goal five minutes before the break when he nodded in Casemiro's delivery.
Benzema went close to a fourth early in the second half when his floated free-kick from 20 yards dropped just over.
To their credit, Cadiz, who started the evening nine points clear of the relegation zone, still tried to take the game to Real and on the hour, substitute Anthony Lozano headed wide from a corner.
Marcelo fired an angled drive straight at the Cadiz goalkeeper after being played in by Benzema, before Real substitute Mariano Diaz broke clear to take the ball around the goalkeeper but shot wide.
In stoppage time, Real goalkeeper Thibaut Courtois denied Cadiz forward Ruben Sobrino a late consolation goal.
The comfortable victory sees Real Madrid move above city rivals Atletico on head-to-head record but having now played a match more, while Barcelona have two in hand.