Some rare sunshine bathed the Court Phillipe Chatrier but it was dull viewing for the few spectators allowed in to watch the 33-year-old glide effortlessly through.
The opening set was done and dusted in 22 minutes as Djokovic won the last 10 points and the second set was only marginally more competitive.
Berankis, ranked 66th, needed courtside treatment on his back before the start of the third set but got back to his feet to endure more punishment from the clinical Serb.
Djokovic, bidding for his second French Open crown and 18th Grand Slam title, has dropped 10 games in two rounds so far and occasionally looked bored, taking the opportunity to practise his drop shot on numerous occasions.
He finished it off after only 83 minutes with his 10th ace.
It was a carbon copy of the pair's only other Grand Slam clash when Berankis also managed only five games, at the 2013 U.S. Open.
It was Djokovic's 70th victory at the French Open, moving him into joint second place on the all-time list with Roger Federer.
Former champion Jelena Ostapenko ousted second seed Karolina Pliskova with a 6-4 6-2 win in the second round after an error-ridden performance from the Czech player.
Latvian Ostapenko, who won the 2017 title as an unseeded player, played aggressively from the start and hit 27 winners as a strangely subdued Pliskova struggled to rein in her unforced errors under the closed roof of Court Philippe Chatrier.
The 23-year-old Ostapenko broke her opponent's serve three times in the first set and twice in the second to seal her victory and ensure that Pliskova remained the only active former world number one who has not won a Grand Slam.
Ostapenko converted her third match point when Pliskova, who had 25 unforced errors, sent a forehand long and she will next meet the winner of the clash between former U.S. Open champion Sloane Stephens and Spaniard Paula Badosa.
Former champion Garbine Muguruza breezed into the third round with a routine 6-3 6-2 victory over Czech Kristyna Pliskova.
It was a welcome stroll on court Suzanne Lenglen for 2016 winner Muguruza, who had fought for three hours in her opening match and needed just over an hour to see off Pliskova.
The Spanish 11th seed made only 13 unforced errors to set up a meeting with American Danielle Collins in the bottom part of the draw where Sofia Kenin is the highest seed - fourth - remaining.
After an early exchange of breaks, Muguruza took full advantage of Pliskova's poor serve - only 42% of first serves in - to bag the opening set.
Pliskova's service rate improved in the second set but Muguruza sprayed the court with winners, making sure there was no comeback for the world number 69.
Canadian ninth seed Denis Shapovalov twice served for the match against Roberto Carballes Baena before losing 7-5 6-7(5) 6-3 3-6 8-6 against the 101st-ranked Spaniard during an absorbing five-hour contest.
Shapovalov served at 5-4 and 6-5 in the deciding set but Carballes Baena levelled the match each time and then broke the Canadian's next service game again to reach the third round of a Grand Slam for the first time in his career.
"It is a dream for me to win a match like this in this court and I think I tried to be very solid and focused on my game," the 27-year-old said in his on-court interview.
"Shapovalov serves very well, he's very aggressive but I think I played a very good match."
The 21-year-old Shapovalov had to script a comeback of sorts of his own to take the match to five sets.
In the first meeting between the two, Carballes Baena broke the Canadian's serve twice to take the opening set.
Shapovalov, considered one of the most talented young players on the men's circuit, left the court for a medical timeout before the eighth game of the second set for what appeared to be a groin issue.
He returned to take the second set, which saw the duo trade double breaks of serve, in a tiebreak but the injury seemed to continue to bother him in the third as his level dropped.
Carballes Baena, who has played 81 of his 110 tour-level matches on clay, dominated the set by winning four of the first five games and appeared to be heading to victory.
But the Canadian came roaring back in the fourth to level the match before suffering the final set heartbreak.
"For me it's just amazing. It's the first time that I won (against) a top-10 player, first time I'm in the third round in a Grand Slam and the first time that I won a match in the fifth set. So I can't be more happy," said Carballes Baena.
Shapovalov hit 65 winners but was undone by an enormous 106 unforced errors. The Spaniard managed 31 winners but kept the errors to 42.
Next up for Carballes Baena will be 18th seed Grigor Dimitrov, who beat Andrej Martin of Slovakia 6-4 7-6(5) 6-1.