I have always found the settlement of MO. very fascinating, and of course, the MO river plays a very central role in that regard.
Around 1805, a series of salt licks were discovered in the central part of the state along the river. Salt, being very important for the preservation of food, was a very valuable commodity at the time. The sons of Daniel Boone began began boiling this brine water down to obtain the salt and shipped it down river to St. Louis, and their salt operation gave this area the name of "The Boonslick," (Boones's Lick). A road opened up from St. Charles, Mo to this region. By 1810, the Fed. Gov. had obtained treaties with the dominate Indian tribe, (the Osage), and the area began to be settled. The war of 1812 disrupted this settlement process, but after the war was over, immigration into the "Boonslick" region boomed. In the center of this area, the town of Franklin was founded in the Mo river bottoms, and within a few years, Franklin became the fastest growing town in MO., (until the MO. river flooded out the town a few years later). This pattern of settlement continued, first westward along the river, and then expanding to the north and south from the river. By the 1830's, the area along the river was pretty well settled, and the rest of the state began to fill in. The river also provided shipping points for the areas further west. The Santa Fe trail originated from Franklin in 1826, but as more people settled westward along the river, these shipping points, the Oregon Trail, the Pony Express, etc. also moved to the western boundary of the State. One of the largest industries on the states' western border was that of freighting to points further west, and this would not have been possible without the river until the railroad was built in the 1850's.
The people who immigrated into the Boonslick area were largely from the states of KY, TN, & VA., and they brought their Southern culture with them. The cash crops they raised were tobacco and hemp, which were sent first to St. Louis and then down to the markets New Orleans. So not only was this region "Southern" in culture, but had strong economic ties with the south. As the settled area along the MO river began to grow, it gained another name, that of "Little Dixie," which shows the southern culture of the area. The political and economic power in the state were also centered along the river, and again, Southern in nature. In the late 1840's, this pattern began to change with a heavy immigration of German settlers into the state, but they tended to settle around St. Louis and the surrounding area, but they were very much pro-Federal in their political views. It's interesting to note that the farther west one goes along the river, the more "southern" the political views of the population.
More directly to the OP's Question-
When the war broke out and Gen. Lyon won the First Battle of Boonville on June 17, 1861, he used the MO river to rapidly move his troops to the center of the state and by winning the battle, forced the MO State Guard all the way down to the Southwest corner of the state. By winning the battle, Lyon was able to keep control of the river which kept the lines of communications, supplies, and troops to and from the western forts open. But more importantly, by controlling the river, Lyon split the southern support in the state in two, which had the dual effect of denying the movement of southern supporters (troops) north of the river from joining MSG south of the river, and driving the political leadership of the state ( the "Little Dixie" region), far away from their base along the river.