Moussa Dembele and Memphis Depay scored either side of Fabregas' dismissal in the first half.
Midfielder Lucas Tousart added a third with 10 minutes remaining against an inexperienced home side who were without former captain Radamel Falcao who is expected to leave the Principality before the end of the transfer window on September 2.
"I said in the week all of three or four opening games will be difficult and Monaco were a difficult opposition, I'm happy with the result," Lyon boss Sylvinho told French broadcasters Canal+.
"I hoped my team would play like this, there's always improvements to be made but I am happy," the former Champions League winner added.
His side showed minimal rustiness despite seeing influential trio in former skipper Nabil Fekir, left-back Ferland Mendy and midfielder Tanguy Ndombele leave during the off-season.
They claimed an early lead with six minutes on the clock with a powerful Dembele header.
The former Celtic forward beat defenders Kamil Glik and Brazilian Jemerson in the air and his effort fizzed past Monaco's Benjamin Lecomte, making his debut for the club.
The home side's best chance of the first half fell to 22-year-old Benjamin Henrichs quarter of an hour later.
He received the ball from winger Gelson Martins, but his low shot failed to trouble Lyon goalkeeper Anthony Lopes.
Things turned from bad to worse for the hosts when experienced playmaker Fabregas was shown a red card for stamping on the back of Leo Dubois' leg on the half hour mark.
In his attempts to chase Dubois down, who was shielding a loose cross out for a goal kick, the Spain midfielder took a stood heavily onto the right-back's calf.
Referee Ruddy Buquet referred the incident to VAR who chose to send Fabregas for an early shower.
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