Despite having their relegation confirmed before kick-off, Granada made an encouraging start to proceedings, forcing Thibaut Courtois to make a couple of important stops.
However, their promising start was quickly forgotten when left-back Fran Garcia produced a side-foot finish to give Real Madrid a 38th-minute lead.
The newly-crowned champions then added a second through Arda Guler to head into the half-time break with a comfortable cushion.
Brahim required just four second-half minutes to take quash any hopes of a Granada fightback with a sublime solo effort.
Just 10 minutes later, the Morocco international netted another goal to register his first La Liga brace and wrap up a comfortable victory.
Los Blancos are now unbeaten in 28 league games, while Granada have now conceded seven goals across their last two matches.
Real Madrid surge into two-goal lead
Real Madrid travelled to Andalusia in a jubilant mood after they produced a dramatic turnaround to beat Bayern Munich in Wednesday's Champions League semi-final second leg.
With the league title already wrapped up, Carlo Ancelotti opted to rotate his starting lineup and rest key players such as Jude Bellingham, Vinicius Junior and Rodrygo.
Ancelotti also made a change in goal, with Courtois coming back into the side to make his second straight start since returning from a long injury layoff.
The Belgium international was forced into action in the 20th minute, tipping the ball over from Bruno Mendez's looping header.
Courtois was then required to make another stop to prevent Carlos Neva's cross from sneaking in at the near post.
After offering very little for the majority of the first period, Real Madrid finally moved through the gears to hit the front in the 38th minute.
Brahim's neat cut-back was dummied by Luka Modric, creating the space for Garcia to tuck home his first goal for Real Madrid's senior side.
Garcia then turned provider for Guler to slide the ball beyond Augusto Batalla, representing his third goal since arriving from Fenerbahce last summer.
Brahim at the double
After doubling their advantage in first-half stoppage time, a hungry Real Madrid side added a third in the opening stages of the second period.
Brahim drove purposefully into the box, before cutting onto his right foot and drilling the ball past Batalla at the near post.
As the game entered the final quarter, the 24-year-old piled more misery on Granada, turning quickly to slide the ball home after being teed up by Modric.
Wednesday's match-winner Joselu spurned a couple of chances to get his own name on the scoresheet, but it mattered little as Los Blancos coasted to their 28th La Liga win of the season.
The Champions have moved onto 90 points with three games to play, while Granada are left languishing in 19th place with just 21 points to their name.
Real Madrid will look to continue their fine run of form when they welcome Alaves to the Santiago Bernabeu on Tuesday.
As for Jose Ramon Sandoval's side, they will attempt to claim their fifth league of the season in Wednesday's away game against Rayo Vallecano.