I think one overlooked strategic victory (although a tactical defeat), that did have an impact on the course of the war was the decision of the new Vicksburg commander, Major General Earl Van Dorn, who took command on June 27, 1862, to assume the offensive following the lifting of the naval siege of Vicksburg by the CSS Arkansas, by then moving against Baton Rouge, the occupied capital of Louisiana. Van Dorn is often characterized as an egocentric, glory seeking and incompetent commander, whose single noteworthy military success came in leading a cavalry raid to destroy Grant's supply depot at Holly Springs in December, 1862. In spite of his personal motives, the decision to move against the Louisiana capital with a combined arms task force and, at the urging of Major General Breckinridge, supported by the formidable ironclad Arkansas, I believe was based on sound strategic planning (if not a firm grasp of ship steam engine mechanics). The criticisms often directed at Van Dorn – that the whole operation was unnecessary and only resulted in unnecessary Confederate losses, including the loss of the irreplaceable ram – I think were largely unjustified, based on an assessment of the results of this campaign.
Two weeks after the battle of Baton Rouge (August 5, 1862), which can certainly be characterized as a Federal tactical victory, the Union forces abandoned the city, its 2,000-man garrison being recalled by Major General Ben Butler who feared New Orleans would be the next target of a Confederate offensive. In this less well-known "sideshow" of the first Vicksburg campaign, Union forces had been "persuaded" to retreat to New Orleans, expecting the next Confederate offensive to be directed toward the liberation of that city, and the departure of all but a token force of gunboats had opened the mouth of the Red River.
Port Hudson, with its 80-foot bluffs, the strongest strategic point on the Mississippi south of Vicksburg, was then occupied without Federal interference, garrisoned and fortified with heavy guns. In fact, Port Hudson did not surrender until after the fall of Vicksburg in July 1863, when the position was rendered untenable, the last Confederate bastion on the river to fall. The presence of Southern forces there withheld needed reinforcements from U. S. Grant's army during his Vicksburg campaign. They did that by keeping Major General Nathaniel P. Banks (who replaced Butler in December, 1862) and his army occupied in siege operations against the Louisiana stronghold. The Port Hudson garrison also held off Federal gunboats trying to travel upriver to join Grant. Because of all these consequences, Van Dorn's campaign prolonged the life of Confederate Vicksburg and the vital connection with the Trans-Mississippi Confederacy.
I'll sum up with a quote by Edwin Bearss, which I think reinforces my point:
"With one ironclad, a handful of guns...the Confederates had regained control of 250 miles of the Mississippi. The failure of Halleck and his Generals to grasp the strategic significance of what was happening on the Mississippi had cost the Union dearly. The first major campaign against Vicksburg had failed...The successful defense of Vicksburg and the recovery of the reaches of the Mississippi between Port Hudson and Vicksburg was a great victory by Confederate arms which had been largely bypassed by military historians."