Fair Fight

[Boromir88]

As hewhoarisesinmight mentions, Morgoth squandered a lot of his power into Arda so he could twist, manipulate, and do what he wanted to it. As is noted in The Silmarillion:

The mightiest of those Ainur who came into the World was in his beginning Melkor...~The Valaquenta

Morgoth would later start squandering his power into Arda to corrupt, to dominate over Men and Elves...etc, and this caused his weakening.

Also, we must look at wording that's used. Tolkien uses 'greatest,' 'mightiest,' 'most powerful,' frequently and you kind of wonder well what does that mean? Melkor being called the 'mightiest' or 'greatest' Vala doesn't mean he is unstoppable and the best at every single attribute. But taking Melkor as a whole he was the 'mightiest.' Let's look at Tulkas:

Greatest in strength and deeds of prowess is Tulkas...He delights in wrestling and tests of strength...~ibid

As far as strength and physical 'prowess' goes Tulkas was called the greatest. This doesn't mean Tulkas was the wisest, fairest,...or any other sort of attribute. But when it came to strength Tulkas was the 'greatest.' You can say that Tulkas was very specialized, he had one trait (strength) where he was the creme-de-la-creme so to say, and that was his specialty.

Being the 'strongest' and taking delight in 'wrestling' it comes as no surprise that he was able to beat Melkor in a wrestling contest. Morgoth was 'great' in several traits (which is probably why in the beginning he was the 'mightiest')...Tulkas was the best at one thing (strength) so in a deeds of strength he was able to beat Melkor. I'm sorry if that's a bit confusing, it's hard for me to get out what I'm trying to say. But try this real-life example if I was too jumbled (I hope your familiar with baseball?):

The best pitcher in baseball is Roger Clemens (I know when we're dealing with this stuff it's debateable, but just bare with me here). Roger Clemens abilities overall and what he's done throughout his career I believe he is the best pitcher.

Joel Zumaya can throw the fastest fastball (he can get into the mid 100's).

Taking this example, eventhough if Clemens is by far the more accomplished and better pitcher...does this mean that if it was a contest of who can throw the fastest that Roger Clemens would beat Joel Zumaya (and everyone else)? No, because Zumaya can throw faster (and indeed he can throw the fastest)...but overall Clemens is a much better pitcher.

Tulkas beat Melkor, because strength and wrestling were Tulkas' specialties but this doesn't make Tulkas the 'greatest' of the Valar.

I hope that helps get across my point a bit more.