The Brazilian side dominated from start to finish on a chilly evening at a half-empty Lincoln Financial Field on Monday, with Esperance managing only two attempts on goal.
Flamengo opened the scoring in the 17th minute when Guillermo Varela surged down the right and delivered a pinpoint cross to Luiz Araujo, who cushioned the ball into the path of Arrascaeta to fire home.
Esperance struggled to get a foothold on the match, with Flamengo enjoying 80 percent possession, but they enjoyed their best moments after the break with Youcef Belaili providing a rare spark.
After curling a shot narrowly wide in the 63rd minute, Belaili forced Flamengo goalkeeper Augustin Rossi into a sharp save with a close-range effort five minutes later.
However, Flamengo quickly reasserted control to silence the lively Tunisian support behind the south goal and in the 70th minute they doubled their lead through Araujo.
Former Chelsea and Arsenal midfielder Jorginho played an incisive through ball for Araujo to break the offside trap and after cutting inside he curled a precise left-footed strike into the bottom corner.
The win puts Flamengo level on points with Chelsea at the top of Group D, after the London club also secured a 2-0 victory over LAFC earlier in the day.
Flamengo and Chelsea meet on Friday in a match likely to determine the group winner. (Reuters)
