Cardiff's last win at Villa Park was in 1954 and the visitors never looked like ending that long drought on Friday.
The home side was on top from the start and Cardiff goalkeeper Ethan Horvath was one of the busiest men on the park.
However, the Welsh club defended stoutly and it took Villa until the middle of the second half to finally get the goal their superiority deserved.
Asensio, the Spanish striker who signed on loan from Paris Saint-Germain in the January transfer window, scored twice in Villa's 2-1 win over Chelsea last week and he continued to justify the faith of coach Unai Emery in only his third start for the club.
The striker took a cut back from the left from Marcus Rashford, another on-loan signing, and slotted home with his left foot.
Twelve minutes later, he did the same but this time from the right, steadying himself to take an Ollie Watkins pass and side-foot home.
"It was not an easy game," Asensio told ITV. "We knew it was a difficult game. (I'm) very happy for the goals, for the win. We're in the next round, that's the most important."
The other fifth-round ties will be played on Saturday and Sunday, followed by the draw for the quarter-finals.
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