[Tuor in Gondolin]

Perhaps the power of Ulmo was able to restrain the Morgulduin influence on the Great River. In Unfinished Tales Ulmo says to Tuor noting his (Ulmo's) ebbing
power in streams near Thangorodrim:

...Doom is strong, and the shadow of the Enemy lengthens; and I am diminished, until in Middle-earth I am become now no more than a secret whisper. The waters that run westward wither, and their springs are poisoned, and my power withdraws from the land

But, of course, his power is based in ocean deep waters and so would naturally extend up the broad Anduin estuary. Sort of like Sauron's noxious gases doing battle with the west winds and swirling around the borders of Mordor during the War of the Ring around Minas Tirith.