Well first off, to be clear, the Mongols did not succeed the Seljuks. After the Seljuks (who collapsed roughly in 1194), came the Khwarezmian Shahdom (originating in Seljuk Transoxania), and a resurgent Abbasid Caliphate, under Caliph al-Nasir. The Seljuks, beset by internal family rivalry, and an expansive Khwarezmian Shahdom, were destroyed, with remnants of their family being found in North West Iran.

When the Mongols did arrive, they met a more or less united Khwarezmian state (after both of them defeated a mutual enemy, the Kara Khitai*), under Shah Muhammad II. But, by the standards of the time, the state was very united, under the strong personality of Shah Muhammad II, who expanded the state quite a bit (except against al-Nasir, where the Khwarezm army was decimated in the Zagros mountains).

But it is still important to remember that the Khwarzem Shahdom did not collapse immediately once the Mongols invaded in the 1210s, and much of Iran resisted and defied Mongol attacks, allowing Muhammad II's successor, Jalal al-Din, to restore Khwarzem authority from Tabriz (in Azerbaijan), and much of Western Iran/Iraq. He was only killed in 1230, but it would not be for some more decades, that Iran was properly pacified, under Hulegu (son of Tolui, who himself was a son of Chinggis Khan).

*Kara Khitai were the largest threat (other than the Ghurids, who had been dealt with) to the Khwarezm Shahs, and were led by a Naiman "exile", who had seized power in their diwan. Naiman being one of the major foes of Chinggis Khan, and his early rise to power.

Source: New Cambridge History of Islam (2010)

If you have any questions, feel free to ask. I tried to keep it as pertinent to your question as possible, but there is a lot more that one can go into :)