The Power to Seal Things on Earth and in Heaven Has Been Given to Every Dispensation

Doctrine and Covenants 128:9–11

9 It may seem to some to be a very bold doctrine that we talk of—a power which records or binds on earth and binds in heaven. Nevertheless, in all ages of  the world, whenever the Lord has given a dispensation of the priesthood to any man by actual revelation, or any set of men, this power has always been given. Hence, whatsoever those men did in authority, in the name of the Lord, and did it truly and faithfully, and kept a proper and faithful record of the same, it became a law on earth and in heaven, and could not be annulled, according to the decrees of the great Jehovah. This is a faithful saying. Who can hear it?
10 And again, for the precedent, Matthew 16:18, 19: And I say also unto thee, That thou art Peter, and upon this rock I will build my church; and the gates of hell shall not prevail against it. And I will give unto thee the keys of the kingdom of heaven: and whatsoever thou shalt bind on earth shall be bound in heaven; and whatsoever thou shalt loose on earth shall be loosed in heaven.
11 Now the great and grand secret of the whole matter, and the summum bonum of the whole subject that is lying before us, consists in obtaining the powers of the Holy Priesthood. For him to whom these keys are given there is no difficulty in obtaining a knowledge of facts in relation to the salvation of the children of men, both as well for the dead as for the living.

President Joseph Fielding Smith wrote:

“What is bound or sealed in the temples of the Lord is also sealed in heaven. This is the great authority which Elijah restored. It also covers ordinances performed for the living as well as for the dead. The Prophet [Joseph Smith] said that all of the ordinances for the living are required in behalf of all the dead who are entitled to the fulness of the exaltation.”

(Church History and Modern Revelation, 2 vols. [1953], 2:329.)