The Madrid youngster had not scored since netting a double against Valencia in August, but he took centre stage in the first-half at the Santiago Bernabeu.
Having already crafted a gilt-edged opening for the equally impressive Isco, Asensio played a major part in Madrid's rather fortunate 18th-minute opener - Paulo Oliveira inadevertently turning in the 21-year-old's cross.
Madrid's second goal 10 minutes later was less fortunate, Asensio hammering in first-time from Isco's sublime cut-back.
While Asensio was on top of his game, the same could not be said of Ronaldo, who squandered a glut of opportunities either side of the break.
Eibar could have made Madrid pay for Ronaldo's poor finishing if the referee had awarded what looked like a stonewall penalty, before substitute Marcelo wrapped up the points in style with eight minutes remaining as Zinedine Zidane's side moved back to within five points of leaders Barcelona.
Isco should have put Madrid ahead inside a minute but, having been picked out by Asensio, the Spain playmaker failed to beat Marko Dmitrovic.
In for the injured Keylor Navas, Madrid's stand-in goalkeeper Kiko Casilla was forced into action soon after - getting down low to keep out Joan Jordan's effort.
Despite a somewhat sluggish opening, however, Madrid soon had their lead, Asensio's cross looping into the top-right corner off the unfortunate Oliveira.
Eibar responded well, Casilla again alert to get down low and prevent Takashi Inui's dipping free-kick creeping in.
Any threat of a quick comeback was swiftly cut short, though - Isco whipping in a low cross that Asensio beautifully swept home on the half volley.
Isco and Asensio combined brilliantly again to tee-up Ronaldo, who failed to apply the finish from close range.
Madrid's playmaking duo were at it again shortly after the restart, Asensio the provider with an inch-perfect throughball into Isco's path, but Dmitrovic pulled off a fine stop.
Casemiro - who had been booked in the first half - was fortunate not to pick up a second yellow card and concede a penalty moments later, as he scythed down Inui in the area.
Ronaldo netted his first LaLiga goal of the season against Getafe last time out, but the Portugal forward could not get the better of Dmitrovic.
And Ronaldo's woes continued late on, the 32-year-old slamming a close-range strike into the side-netting, before Marcelo took matters into his own hands.
Fellow substitute Karim Benzema slipped through a brilliant pass - Marcelo spinning clear of his marker to plant a low finish across Dmitrovic and add gloss to the victory.
Key Opta Facts:
- Marco Asensio has scored four goals in his five games against Eibar in La Liga, his favourite opponent in the competition.
- Isco Alarcon has scored more goals (10) and made more assists (8) than any other midfielder in La Liga in 2017.
- Cristiano Ronaldo (33) and Karim Benzema (14) have attempted 47 shots in La Liga this season but only two have ended up in goals.
- Karim Benzema has made 59 assists in La Liga since his Real Madrid arrival - only Lionel Messi (113) and Cristiano Ronaldo (83) have more among all the striker since then.
- Cristiano Ronaldo had as many shots (five) as the number of touches in the opposite box (five) against Eibar.