Vinicius Jr gave the champions the lead just before halftime with a long-range shot but the visitors equalised after the break through Kike Garcia, who scored with a brilliant header from the edge of the area that looped over the goalkeeper.
Benzema fired his penalty off the bar and over in the 79th minute, after being fouled inside the area by defender Unai Garcia, who was shown a straight red card after a VAR check.
The France striker had a goal chalked off a minute later for offside and Vinicius had a bullet shot kept out by Sergio Herrera a little later, as Real Madrid pressed for the win.
Osasuna, however, held on to take a point to the frustration of the home fans.
🎙️ @MrAncelotti : “The game was under control and we deserved to win.”#RealMadridOsasuna. https://t.co/w6RbaoWrSS
— Real Madrid C.F. 🇬🇧🇺🇸 (@realmadriden) 1664748589000
Real Madrid are level with rivals Barcelona on 19 points at the top of standings, with Barca ahead on goal difference.
The point at Santiago Bernabeu lifted Osasuna to sixth on 13 points.
Real Madrid manager Carlo Ancelotti had a major selection headache after Croatia midfielder Luka Modric reported back from international duty nursing an injury and goalkeeper Thibaut Courtois was a surprise late omission after suffering with a nerve problem in his back.
On the positive side, Benzema made his long-awaited comeback after three weeks out with a right knee injury.
The striker was lively up-front alongside Vinicius Jr and almost scored early in the first-half from a cross by the Brazilian, firing a splendid first-time volley that went narrowly wide of the left post.
Ukrainian goalkeeper Andriy Lunin proved a solid replacement for Courtois, denying efforts by Jon Moncayola and Ez Abde in the first half.
But it was Vinicius who gave Real Madrid the lead with what looked like a lucky effort from distance.
The Brazil international whipped a cross from just outside the left corner of the box towards the back post, but it evaded everyone and somehow ended up going all the way into the net as the goalkeeper took too long to react.
Antonio Rudiger and Benzema were in offside positions and moved for the ball, but the goal stood after a VAR check.
Osasuna found the equaliser five minutes after the break and held on until Garcia fouled Benzema in the six-yard box.
The referee did not initially award the penalty, but changed his mind after checking the VAR footage, showing a red card to the Osasuna defender.
Benzema, however, sent his penalty kick off the crossbar and over.
“We deserved the win but we missed a penalty. It’s normal, setbacks happen. This is football,” Ancelotti told reporters.
“Benzema has done his part, he had the penalty chance after a very good play but missed it. It’s an accident that sometimes happens. We have to move forward.”