DAMN YOU FOR THAT TV TROPES LINK!
OT: I think the Covenant were a bit played up with the overall feeling of hopelessness. They make it seem like the war was swift and bloody, when really it was a lot of waiting for the Covies to find another planet to 'splode.
The Covenant had the technological advantage, certainly. The only reason the humans had a chance was because of the NOVA bomb. It basically took out half the Elites, so they were forced to shack up with humanity if they wanted to defeat the Prophets and Brutes. This joining of forces helped deal with Truth at Earth, and later the Battle at the Ark. Luckily, the majority of the Loyalists were at the Ark, where the now decimated allies were headed, but still helping to keep the heat off of Earth. They managed to have a Mock Guffin scenario where they blew up the entrenched Loyalists who were trying to activate the Ark.
Overall, humanity won, but by the tiniest sliver of luck. If the NOVA hadn't been a thing, then the Elites would have had a massive fleet and plenty of soldiers to eliminate the Prophets and the humans. Perhaps they might fall in the end to the Loyalists, but that never occurred so we will never know.