Superman is actually the closest thing that Darkseid has to an arch rival and an equal. The two are evenly matched and their fights often reflect that. They are pretty much 50/50 in terms of hand to hand combat and have traded victories every time they tussled.
In some instances, Darkseid proves to be too powerful in the moment and Supes has to call for help from the Justice League; this was the case in Final Crisis. Other times, The Man of Steel is able to come out on top, but solely and simply out of pure luck to find a way to deal the final blow.
One encounter that fans may remember best came in the series finale to the Superman Animated Series. The two basically fought to the death until Supes just barely won by the skin of his teeth.
Superman did not simply defeat Darkseid due to being stronger or necessarily better, but out of sheer will and motivation. Darkseid had pummeled The Last Son of Krypton for several minutes and promised to kill more people after ending the Kryptonian's life. In a last ditch effort, Superman clasped Darkseid's eyes just as he was ready to unleash a bevy of eye beams.
After Darkseid essentially blasted himself in the face, he was too weak to fight anymore. The Man of Tomorrow then left Darkseid on his home planet to rot with his followers.