In a game played at a nearly empty Ahmad bin Ali Stadium in Qatar, the Copa Libertadores champions capitalised on a series of defensive lapses by Cruz Azul to secure victory.
Arrascaeta opened the scoring in the 15th minute after Cruz Azul defender Gonzalo Piovi gifted him the ball with a misplaced pass inside his own penalty area. Unmarked, the Uruguayan effortlessly dribbled past the goalkeeper before slotting the ball into an empty net.
Cruz Azul responded, dominating possession in pursuit of an equaliser. They thought they had levelled the match in the 42nd minute when Gabriel Fernandez found the back of the net, but the goal was ruled out for offside.
Two minutes later, Jorge Sanchez delivered the breakthrough for the Mexicans with a stunning volley from the edge of the area after Flamengo's Jorge Carrascal failed to clear his lines.
The second half saw both sides create chances and battle for control, but it was Flamengo who found the winner in the 71st minute.
Arrascaeta surged down the left wing and delivered a low ball into the area that was only partially cleared and the Uruguayan latched onto it, lofting a sublime chip over the diving keeper.
Despite Piovi's desperate attempt to clear, goal-line technology confirmed the ball had crossed, giving Flamengo the lead.
Flamengo then held on to their advantage despite Cruz Azul's spirited late push, with Agustin Rossi making key saves to deny further opportunities.
The Brazilian outfit will now prepare for Saturday's semi-final against Pyramids, aiming to book their place in a showdown with Paris St Germain in the tournament's final.