I didn't know that happened. I do know that Standard Oil took a huge advantage in economies of scale and scope, that allowed it to drastically lower its cost compared to potential competitors. If Standard Oil did drop prices as you claim, then they valued market share over pricing in order to maximize revenue. If they continued to lower their prices, then competitors, who would have naturally higher costs, wouldn't be able to compete and would have to leave the market, allowing Standard Oil to occupy even larger market share. If the amount of petroleum they sold increased faster than the price drop (through increasing market share and generally increasing demand as the market for petroleum grew very quickly as Standard Oil developed), then Standard Oil would see its profits balloon, while competitors would face intractable barriers to entry.
In all, with a naturally growing market in petroleum and lower relative costs compared to competitors, Standard Oil preferred to maximize market share over optimal price setting in order to erect more barriers to entry for potential competitors by setting artificially low prices.
Whether something is a monopoly or not depends on how broadly you define the market. Eg J. K. Rowling has a monopoly on the 'real' Harry Potter story (no disrespect to fan fic authors), a small share of the book market, and a tiny share of the entertainment market.
Standard Oil was not just competing against other oil producers, but other energy sources (eg coal, water power, horse power, good old walking), and even competing against things statisticians don't classify as energy. For example if you are building a factory and transport is expensive you're more likely to use local building materials than if transport is cheap. If you're deciding what to do with a free evening then driving into town to watch a movie competes with having the neighbours round for a game of poker.
To go back to the J. K Rowling example, I noticed that when she got very popular, when a new Potter book came out it would sell at a discount to normal hardback prices. Presumably the booksellers decided that they could get higher profits by selling more Potter books to people who, at a higher price, might have waited to read someone else's copy than the money the booksellers forwent by not selling copies at a very high price to those fanatical fans who'd mortgage the cat to get their next Potter fix.
To put it another way, calling a business a monopoly is a social construction highly dependent on what you call a market.
[Edit to add: George R. Hall, Market Definition and Antitrust Policy, 20 Wash. & Lee L. Rev. 47 (1963), http://scholarlycommons.law.wlu.edu/wlulr/vol20/iss1/4 has a reasonably accessible discussion of some of the issues American courts have grappled with in defining markets under anti-trust laws. It is a 1960s paper but the more recent studies I'm aware of tend to look a lot more to econometric data and thus are less readable.]