Benzema had a busy afternoon, being denied first by Marko Dmitrovic as he looked to round the goalkeeper, and then by the offside flag when he headed home Marcelo's cross. Asensio hit the crossbar with a free kick, and then had a goal ruled out as he was offside when diverting Isco's shot past Dmitrovic, before he clinically opened the scoring from Casemiro's pass.
Asensio went close to a second after half-time, Dmitrovic tipping his dipping shot over the bar, and then Thibaut Courtois reacted quickly to prevent Lucas Vazquez's bac-kpass finding his own net. Casemiro became the latest Madrid player to have a goal cancelled out by the offside flag before Benzema's header from substitute Vinicius Junior's cross secured the three points.
One false move in this 10-game final stretch of the season and Real Madrid's title hopes will go up in smoke, leaving Barcelona and Atletico Madrid to battle it out. Here, they got the required win when nothing else would do, and in some style, too, as they move into a defining 12-day period that will see them go on to face Liverpool, Barca and then Liverpool again.
It feels like we've been waiting a long, long time for Asensio to fulfil his undoubted enormous potential. This was probably the 25-year-old's best performance of the season -- scoring, having a goal ruled out for offside, hitting the woodwork -- and you'd like to think it could serve as a springboard for an influential end-of-campaign run. But maybe that's wishful thinking.
There was a brief second-half spell at 1-0, with Madrid coming under pressure as the wind blew, the rain and hail fell, and Eibar grew in confidence, when this result looked in doubt. Fortunately for them, it didn't last long, and Benzema's goal ended the game as a contest.
Manager rating out of 10
8 -- Zinedine Zidane picked an intriguing team, with Ferland Mendy and Marcelo both in the starting XI. That meant Nacho, Eder Militao and Mendy in a back three, with Marcelo at wing-back, while Isco and Asensio flanked Benzema in attack and Raphael Varane and Toni Kroos were left on the bench. The team played well and could have led long before Asensio's breakthrough before half-time, while Zidane's second-half changes brought some freshness to the team when they needed it.
Player ratings (1-10; 10 = best. Players introduced after 70 minutes get no rating)
GK Thibaut Courtois, 7 -- Made a good early save from Pape Diop, and then did superbly well to recover when Vazquez's second-half back-pass threatened an own-goal when it was caught by the wind and rain.
DF Lucas Vazquez, 7 -- Had a potentially tricky afternoon against La Liga's most exciting young wide player, Bryan Gil, but managed to turn the tables, beating the youngster and seeing him carded in the first half.
DF Eder Militao, 7 -- Didn't look as uncomfortable as he often has in a Real Madrid shirt. Playing in a back three, rather than a pair, leaves him less vulnerable to getting caught one-on-one.
DF Nacho, 7 -- Seems to enjoy his leadership role when Ramos is absent. Anchored the defence well from the middle of the back three.
DF Ferland Mendy, 7 -- Certainly has the attributes to perform as a left-sided centre-back, even if that means curbing his attacking instincts.
DF Marcelo, 7 -- A busy start, as much of Madrid's threat came from the left-hand side, including a super cross for Benzema's offside header. Enjoys playing in a more advanced position with the security of Mendy behind him.
MF Casemiro, 8 -- The holding midfielder tag is entirely inadequate now, given the variety of the Brazilian's talents and his involvement in almost every aspect of the team's play. Won the ball and provided the assist for Asensio. Thought he'd scored later, before the offside flag went up.
MF Luka Modric, 7 -- Played all three of Croatia's games during the international break, starting two of them, and so was understandably taken off after an hour. One delightful first-half nutmeg.
MF Isco, 7 -- Started on the left, with freedom to move inside, and put in one of his better displays this season. Played a part in Asensio's offside goal and was frequently involved in Madrid's play. Only a mis-control denied him a second-half goal.
FW Marco Asensio, 8 -- Encouraging. Took up more-central positions and thrived as a result. Hit the bar with 20 minutes played and was then unfortunate to see his smartly taken goal ruled out for offside. The goal that did stand was a marvel of technique, with two perfect touches to control and finish.
FW Karim Benzema, 8 -- Dangerous early on, almost managing to round Dmitrovic and then heading in from an offside position, before scoring a second-half header to make it nine goals in his past seven games in all competitions.
MF Toni Kroos, 6 -- Played the last half hour when fresh legs were required.
FW Rodrygo, 6 -- Came on with Kroos, replacing Asensio.
FW Vinicius Junior, 7 -- An excellent run and cross for Benzema's goal, just when the team needed a second goal.
FW Sergio Arribas, 7 -- Looks tidy, composed and promising every time he comes on.
FW Mariano, N/R -- Didn't have much time to contribute.