In the 19th century, the third holiest mosque in Islam was....The Mosque of Quba.

According to A Dictionary of Islam: Being a Cyclopædia of the Doctrines, Rites, Ceremonies, and Customs, Together with the Technical and Theological Terms, of the Muhammadan Religion by Thomas Patrick Hughes (1885):

MASJIDU 'T-TAQWA. Lit. "The Mosque of Piety." The mosque at Quba', a place about three miles south-east of al-Madinah. It was here that it is said that the Prophet's camel, alQaswa rested on its way from Makkah to alMadinah, on the occasion of the Flight. And when Muhammad desired the Companions to mount the camel, Abu Bakr and • Umar did so, but she still remained on the ground; but when 'Ali obeyed the order, she arose. Here the Prophet decided to erect a place for prayer. It was the first mosque erected in Islam. Muhammad laid the first brick, and with an iron javelin marked out the direction for prayer. The Prophet, during his residence at al-Madinah, used to visit it once a week on foot, and he always made a point of praying there the morning prayer on the 17th of Ramazan. A prayer in the mosque of Quba' is said to be equal in merit to a Lesser Pilgrimage to Makkah, and the place itself bears rank after the mosques of Makkah and alMadinah and before that of Jerusalem. It was originally a square building of very small size, but the Khalifah 'Usman enlarged it. Sultan 'Abdu '1-Hamid rebuilt the place, but it has no pretensions to grandeur. (See Burton's Pilgrimage, vol. i. p. 890;)

The encyclopedia dedicates the following amount of space to these important mosques:

Mosque L' Haram (Mecca) - 21 columns
Mosque N' Nabi (Medina) - 5 columns
Mosque T-Taqwa (Quba) - 1/2 column
Mosque Al Aqsa (Jerusalem) - 1/3 column

It appears that the Al Aqsa Mosque was not considered the third holiest spot in Islam until the 20th century.