Standard Oil's market share peaked at over 50%. There are various ways to measure market share: production, final retail sales, gallons pumped, etc. There is no doubt the that company was huge, and its large market share allowed it to impact prices. But given the presence of competitors, Standard Oil did not have complete control over the market.
When a company is as big as Standard Oil, two problems arise: there is a lot more room for waste and inefficiency, which means that your competitors have a chance of underpricing you; being the biggest, you are the primary target for all competitors. Both of these factors began to take Standard Oil down, before the federal government took any action. Thomas Woods writes:
the federal government moved to dissolve Standard Oil during Theodore Roosevelt's presidency. But by the time the federal government dissolved Standard Oil in 1911, the company's market share had already been reduced to 25 percent as a result of normal market competition.
Different historians give different numbers regarding Standard Oil's market share, but all agree that its market share fell significantly, and long before the Supreme Court ruling began to appear likely.
historian Gabriel Kolko notes that from 1899, Standard Oil had "entered a progressive decline in its control over the oil industry, a decline accelerated, but certainly not initiated, by the dissolution." Standard's decline, Kolko explains, was "primarily of its own doing - the responsibility of its conservative management and lack of initiative."
If a market is free enough - unfettered by regulation - it will keep itself in order, even to the point of dismantling companies which threaten to approach monopoly status. By contrast, only with the the help of government intervention and regulation can a company become a true monopoly with 100% market share.