Real had drawn level at the weekend with arch-rivals Barcelona, which held the previous record of 39 games in a row without a defeat.
Zidane's team have advanced to the quarter-finals of the Copa del Rey, on a 6-3 aggregate score.
Sevilla deserved better on a night they deliver a hugely energised performance and with Real resting most of their stars.
The hosts opened the score on an own goal by Danilo as early as the ninth minute and that bolstered their belief that turning around the 3-0 deficit from the first leg at the Bernabeu was possible.
A great goal by Marco Asensio two minutes into the second half dumped the mood in Seville but Jovetic, on his debut night, still put the hosts ahead again with a volley in the 53rd minute.
Sevilla missed a host of chances until finally Iborra managed to score the third in the 77th minute. The hosts needed two more goals to go through but rather than stunning Real they were left without even the joy of victory.
Casemiro won a penalty in the 83rd minute which Sergio Ramos executed Panenka-style to make it 3-2 and in the final seconds of the three-minute stoppage time, when everyone thought the game was all but over, Benzema came out of nowhere to score the third and preserve Real's unbeaten run.