Lewandowski opened the scoring in the 10th minute from the penalty spot, finding the back of the net for the 100th time in the Champions League, and he joined Lionel Messi and Cristiano Ronaldo as the only players to score a century of goals in the competition.
Dani Olmo scored the Spanish side's second of the game in the 66th minute after receiving the ball inside the penalty area after a square cross from Gerard Martin, and the goalscorer's danced past centre-back Brendan Chardonnet before firing his shot off of Brest goalkeeper Marco Bizot and into the net.
Lewandowski scored his side's third of the match in second-half stoppage time when he collected a driven pass into the penalty area from Alex Balde with one touch, before stroking the ball into the bottom-right corner with his second touch.
The result means that Barca are now second with 12 points from their five outings in the Champions League and are just one point from first-placed Inter Milan.
Meanwhile, Brest are ninth with 10 points but have the same amount of points as every team above them up until fifth-placed Bayer Leverkusen.
Barca's Polish striker was awarded a penalty in the opening stages of the game when he was clattered by Brest goalkeeper Bizot after Dani Olmo crossed into the box, and Lewandowski calmly converted following a stuttered run up.
While Martin's low delivery was excellent for Olmo's goal, the attacker deserves most of the credit given his close control inside the penalty area, though Bizot should have done better given the ball bounced off him and into the back of the net.
Lewandowski demonstrated his immense composure in the box when he scored his second of the game, with the striker shielding the ball before swivelling his body and striking home.
BARCELONA VS. BREST HIGHLIGHTS
Robert Lewandowski goal vs. Brest (10th min, Barcelona 1-0 Brest)
Brest goalkeeper Marco Bizot bizarrely fouls Robert Lewandowski when trying to claim a cross, and the Barca striker calmly converts the resulting penalty, slotting the ball to the right side of the net!
Dani Olmo goal vs. Brest (66th min, Barcelona 2-0 Brest)
Gerard Martin fires a low cross to Dani Olmo, who takes the ball while charging into the box, and his close control allows him to beat centre-back Brendan Chardonnet before he shoots at goal, scoring despite his effort striking goalkeeper Bizot!
Robert Lewandowski goal vs. Brest (92nd min, Barcelona 3-0 Brest)
Alex Balde picks up the ball on the left of Brest's penalty area and finds Lewandowski in the box, and the striker controls the ball on his right foot in a central position before he swivels his hips and gently guides the ball into the bottom-right corner!
MAN OF THE MATCH - ROBERT LEWANDOWSKI
Robert Lewandowski might be into his mid thirties, but the legendary striker proved once again that he still has so much to offer, scoring his 100th Champions League goal.
Perhaps more impressive was the Polish striker's general play, with the forward always presenting himself as an option for teammates.
The 36-year-old might no longer be the quickest, but he displayed his intelligence in and around the box against Brest, and the veteran was still able to contribute positively to Hansi Flick's intense out of possession system.
BARCELONA VS. BREST MATCH STATS
Possession: Barcelona 76%-24% Brest
Shots: Barcelona 19-2 Brest
Shots on target: Barcelona 8-0 Brest
Corners: Barcelona 4-0 Brest
Fouls: Barcelona 8-19 Brest
BEST STAT
WHAT NEXT?
Barcelona are set to take on Las Palmas on Saturday in La Liga, before playing Mallorca away from home in early December.
As for Brest, they will host Strasbourg on November 30 in Ligue 1, with their subsequent match against Lille in the French top flight to come on December 6.